1. Find the interest rate on a loan charging $1292 simple interest on a principal of $4750 after 8 years.

%

2. Find the term of a loan of $200 at 4.5% if the simple interest is $36.

3. Determine the amount due on the compound interest loan. (Round your answers to the nearest cent.)

$18,000 at 5% for 15 years if the interest is compounded in the following ways.

(a) annually

$

(b) quarterly

$

4. Calculate the present value of the compound interest loan. (Round your answers to the nearest cent.)

$24,000 after 8 years at 3% if the interest is compounded in the following ways.

(a) annually

$

(b) quarterly

$

5. Find the term of the compound interest loan. (Round your answer to two decimal places.)

4.9% compounded quarterly to obtain $8100 from a principal of $2000.

6. Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your answers to two decimal places.)

8% compounded annually.

"rule of 72"	yr
exact answer	yr

7. Find the effective rate of the compound interest rate or investment. (Round your answer to two decimal places.)

28% compounded monthly. [Note: This rate is a typical credit card interest rate, often stated as 2.3% per month.]

%

8. Since 2007, a particular fund returned 13.1% compounded monthly. How much would a $5000 investment in this fund have been worth after 2 years? (Round your answer to the nearest cent.)

$

9. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.

Find the accumulated amount of the annuity. (Round your answer to the nearest cent.)

$3500 annually at 7% for 10 years.

$

10. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.

Find the required payment for the sinking fund. (Round your answer to the nearest cent.)

Monthly deposits earning 5% to accumulate $7000 after 10 years.

$

11. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.

Find the amount of time needed for the sinking fund to reach the given accumulated amount. (Round your answer to two decimal places.)

$2500 yearly at 7% to accumulate $100,000.

12. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.

An individual retirement account, or IRA, earns tax-deferred interest and allows the owner to invest up to $5000 each year. Joe and Jill both will make IRA deposits for 30 years (from age 35 to 65) into stock mutual funds yielding 9.7%. Joe deposits $5000 once each year, while Jill has $96.15 (which is 5000/52) withheld from her weekly paycheck and deposited automatically. How much will each have at age 65? (Round your answer to the nearest cent.)

Joe		$
Jill		$

???????

13. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.

How much must you invest each month in a mutual fund yielding 11.5% compounded monthly to become a millionaire in 10 years? (Round your answer to the nearest cent.)

$

???????

14. Calculate the present value of the annuity. (Round your answer to the nearest cent.)

$17,000 annually at 5% for 10 years.

$

15. Determine the payment to amortize the debt. (Round your answer to the nearest cent.)

Monthly payments on $160,000 at 5% for 25 years.

$

16. Determine the payment to amortize the debt. (Round your answer to the nearest cent.)

Quarterly payments on $14,500 at 3.1% for 6 years.

$

17. Find the unpaid balance on the debt. (Round your answer to the nearest cent.)

After 7 years of monthly payments on $170,000 at 4% for 25 years.

$

18. The super prize in a contest is $10 million. This prize will be paid out in equal yearly payments over the next 20 years. If the prize money is guaranteed by AAA bonds yielding 4% and is placed into an escrow account when the contest is announced 1 year before the first payment, how much do the contest sponsors have to deposit in the escrow account? (Round your answer to the nearest cent.)

$

1. Find the interest rate on a loan charging $1292 simple interest on a principal of $4750 after 8 years. % 2. Find the term of a loan of $200 at 4.5% if the simple interest is $36. 3. Determine the amount due on the compound interest loan. (Round your answers to the nearest cent.) $18,000 at 5% for 15 years if the interest is compounded in the following ways. (a) annually $ (b) quarterly $ 4. Calculate the present value of the compound interest loan. (Round your answers to the nearest cent.) $24,000 after 8 years at 3% if the interest is compounded in the following ways. (a) annually $ (b) quarterly $ 5. Find the term of the compound interest loan. (Round your answer to two decimal places.) 4.9% compounded quarterly to obtain $8100 from a principal of $2000. 6. Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your answers to two decimal places.) 8% compounded annually. "rule of 72" yr exact yr answer 7. Find the effective rate of the compound interest rate or investment. (Round your answer to two decimal places.) 28% compounded monthly. [Note: This rate is a typical credit card interest rate, often stated as 2.3% per month.] % 8. Since 2007, a particular fund returned 13.1% compounded monthly. How much would a $5000 investment in this fund have been worth after 2 years? (Round your answer to the nearest cent.) $ 9. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. Find the accumulated amount of the annuity. (Round your answer to the nearest cent.) $3500 annually at 7% for 10 years. $ 10. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. Find the required payment for the sinking fund. (Round your answer to the nearest cent.) Monthly deposits earning 5% to accumulate $7000 after 10 years. $ 11. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. Find the amount of time needed for the sinking fund to reach the given accumulated amount. (Round your answer to two decimal places.) $2500 yearly at 7% to accumulate $100,000. 12. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. An individual retirement account, or IRA, earns tax-deferred interest and allows the owner to invest up to $5000 each year. Joe and Jill both will make IRA deposits for 30 years (from age 35 to 65) into stock mutual funds yielding 9.7%. Joe deposits $5000 once each year, while Jill has $96.15 (which is 5000/52) withheld from her weekly paycheck and deposited automatically. How much will each have at age 65? (Round your answer to the nearest cent.) Joe $ Jill $ 13. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. How much must you invest each month in a mutual fund yielding 11.5% compounded monthly to become a millionaire in 10 years? (Round your answer to the nearest cent.) $ 14. Calculate the present value of the annuity. (Round your answer to the nearest cent.) $17,000 annually at 5% for 10 years. $ 15. Determine the payment to amortize the debt. (Round your answer to the nearest cent.) Monthly payments on $160,000 at 5% for 25 years. $ 16. Determine the payment to amortize the debt. (Round your answer to the nearest cent.) Quarterly payments on $14,500 at 3.1% for 6 years. $ 17. Find the unpaid balance on the debt. (Round your answer to the nearest cent.) After 7 years of monthly payments on $170,000 at 4% for 25 years. $ 18. The super prize in a contest is $10 million. This prize will be paid out in equal yearly payments over the next 20 years. If the prize money is guaranteed by AAA bonds yielding 4% and is placed into an escrow account when the contest is announced 1 year before the first payment, how much do the contest sponsors have to deposit in the escrow account? (Round your answer to the nearest cent.) $ 1. Find the interest rate on a loan charging $1292 simple interest on a principal of $4750 after 8 years. % Let the rate be "r". Using the formula SI = P*R*T 1292 = 4750*r*8 or r = 1292/(4750*8) or r = 0.034 or 3.4% 2. Find the term of a loan of $200 at 4.5% if the simple interest is $36. 36=200*T*4.5/100 T=4 3. Determine the amount due on the compound interest loan. (Round your answers to the nearest cent.) $18,000 at 5% for 15 years if the interest is compounded in the following ways. (a) annually $ V = P(1+r)^nt V=18,000(1+0.05)^15=37,420.71 (b) quarterly $ V = P(1+r)^nt V=18,000(1+0.05/4)^(4*15)=37,929.26 4. Calculate the present value of the compound interest loan. (Round your answers to the nearest cent.) $24,000 after 8 years at 3% if the interest is compounded in the following ways. (a) annually $ PV=FV/(1+r)^n PV=24,000/(1.03)^8=18945.82 (b) quarterly $ PV=FV/(1+r)^n*t PV=24,000/(1.03)^8*4=9320.09 5. Find the term of the compound interest loan. (Round your answer to two decimal places.) 4.9% compounded quarterly to obtain $8100 from a principal of $2000. Compound Interest: A = P(1+r) ^nt; where: P = initial amount deposited. r= rate of interest; n=number of times the interest is compounded quarterly t =total time span i.e. 8100 = 2000 (1+0.049/3) ^3t; 4.05 = (1.016) ^t; ln (4.4)/ln (1.016) = t; i.e t= 88.1173 6. Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your answers to two decimal places.) 8% compounded annually. "rule of 72" exact answer yr yr To find the rule of 72 to estimate the doubling time for interest rate, then calculate it at 8%compounded annually R*t=72 T=R/72 T=72/8=9 Double the money in 9 years at 8% 1.08^9=1.999 which is approximately 2 7. Find the effective rate of the compound interest rate or investment. (Round your answer to two decimal places.) 28% compounded monthly. [Note: This rate is a typical credit card interest rate, often stated as 2.3% per month.] % 28% compounded monthly. Let the effective rate of interest be Reff 1+ Reff=(1+r/12)^12=(1+0.28/12)^12=1.31889 So Reff=31.89% 8. Since 2007, a particular fund returned 13.1% compounded monthly. How much would a $5000 investment in this fund have been worth after 2 years? (Round your answer to the nearest cent.) $ Amount after 2 years= A=P(1+r)^nt A=5000(1+0.131/12)^(12*2)=22,922.02 9. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. Find the accumulated amount of the annuity. (Round your answer to the nearest cent.) $3500 annually at 7% for 10 years. $ Future value of annuity = C * [(1+i)^n -1]/i C = payment per period = 3500 interest rate per period = 7% number of periods = 10 accumulated amount FV = 3500 * [(1+7%)^10 -1]/7% = $48,357 10. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. Find the required payment for the sinking fund. (Round your answer to the nearest cent.) Monthly deposits earning 5% to accumulate $7000 after 10 years. $ The formula for SINKING FUND is given by S =R[(1+i)^n - 1] / i Here given S=8000, i=5% monthly=5/100 *12=0.05/12=1.256 * 10^-5, n= 12x10=120 Required amount for sinking fund(R)= S * i /(1+i)^n - 1 =7000 * 1.256 x 10^-5 /[(1+1.256 x 10^-5)^120 - 1] =0.10048 / 1.5083 x 10-3 =58.29 11. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. Find the amount of time needed for the sinking fund to reach the given accumulated amount. (Round your answer to two decimal places.) $2500 yearly at 7% to accumulate $100,000. 100,000=2500((1+0.07)^n-1)/0.07 40*0.07+1=(1+0.07)^n 3.1=(1+0.07)^n Log3.8=nlog1.07 N=log3.8/log1.07=20 12. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. An individual retirement account, or IRA, earns tax-deferred interest and allows the owner to invest up to $5000 each year. Joe and Jill both will make IRA deposits for 30 years (from age 35 to 65) into stock mutual funds yielding 9.7%. Joe deposits $5000 once each year, while Jill has $96.15 (which is 5000/52) withheld from her weekly paycheck and deposited automatically. How much will each have at age 65? (Round your answer to the nearest cent.) Joe $ Jill $ A J Yearly investment amount is $5,000 Number of deposits are(65-35)30 Yield =9.7% Jack deposits $5,000 once each year while Jill has $ 96.16($5,000/52) FV for Jack Annuity value=5,000*[(1.097)^30-1/0.097] =777,153.15 FV for Jill Jill deposit $96.15 by weekly. Total number of weeks is 52 Total deposits are (30 years *52 weeks)1,560 Annuity future value=96.15*[(1+9.7%/52)^1560 -1]/0.001865385] Fv=892,083.13 13. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. How much must you invest each month in a mutual fund yielding 11.5% compounded monthly to become a millionaire in 10 years? (Round your answer to the nearest cent.) $ A answer is 14. Calculate the present value of the annuity. (Round your answer to the nearest cent.) $17,000 annually at 5% for 10 years. $ Present value of annuity=p(1-(1+r)^-nt)/r 17,000(1-1.05^-10)/0.05=131269.49 15. Determine the payment to amortize the debt. (Round your answer to the nearest cent.) Monthly payments on $160,000 at 5% for 25 years. $ We use the above formula P=$160000 r=5% n=25*12=300 A=160,000*0.05(1.05)^300 (1+0.05)^300-1 A=8000 16. Determine the payment to amortize the debt. (Round your answer to the nearest cent.) Quarterly payments on $14,500 at 3.1% for 6 years. $ We use the above formula P=$14500 r=3.1% n=6*4=24 A=14,500*0.031(1.031)^24 (1+0.031)^24-1 A=865.44 17. Find the unpaid balance on the debt. (Round your answer to the nearest cent.) After 7 years of monthly payments on $170,000 at 4% for 25 years. $ use pmt formulae in excel to find the monthly payment pmt(rate,nper,pv,fv,type) =PMT(5%/12,25*12,-150000,,0)=$876.89 18. The super prize in a contest is $10 million. This prize will be paid out in equal yearly payments over the next 20 years. If the prize money is guaranteed by AAA bonds yielding 4% and is placed into an escrow account when the contest is announced 1 year before the first payment, how much do the contest sponsors have to deposit in the escrow account? (Round your answer to the nearest cent.) $ C = Cash flow per period = 10000000/20 = 500000 i = interest rate n = number of payments PV = 500000 * [1 - (1+0.04)^-25]/0.04 =7811039.97