Future Value: The future value of the deposit after 5 years can be calculated using the formula:

FV = PV x (1 + r)^n

Where: PV = $2,000,000 (the present value or initial deposit) r = 6% (the annual interest rate) n = 5 (the number of years)

FV = $2,000,000 x (1 + 0.06)^5 = $2,835,730.92

Therefore, the amount in the account after 5 years will be $2,835,730.92.

Present Value: The present value of the security can be calculated using the formula:

PV = FV / (1 + r)^n

Where: FV = $29,000 (the future value of the security) r = 5% (the annual interest rate of securities of equal risk) n = 20 (the number of years)

PV = $29,000 / (1 + 0.05)^20 = $10,423.59

Therefore, the present value of the security is $10,423.59.

Required Interest Rates: The required annual interest rate can be calculated using the formula:

r = (FV / PV)^(1) - 1

Where: PV = $350,000 (the present value or initial deposit) FV = $800,000 (the desired future value) n = 19 (the number of years)

r = ($800,000 / $350,000)^(1/19) - 1 = 5.13%

Therefore, the owner must earn an annual interest rate of 5.13% to reach her retirement goal.

Future Value of an Annuity: For an ordinary annuity with compounding occurring once a year, the future value can be calculated using the formula:

FV = PMT x [(1 + r)^n - 1] / r

Where: PMT = the amount of each payment r = the annual interest rate n = the number of payments

a. $500 per year for 8 years at 14% FV = $500 x [(1 + 0.14)^8 - 1] / 0.14 = $7,712.99

b. $250 per year for 4 years at 7% FV = $250 x [(1 + 0.07)^4 - 1] / 0.07 = $1,115.63

c. $700 per year for 4 years at 0% FV = $700 x [(1 + 0)^4 - 1] / 0 = $2,800

Therefore, the future values of the annuities are $7,712.99, $1,115.63, and $2,800, respectively.

Present Value of an Annuity: For an ordinary annuity with discounting occurring once a year, the present value can be calculated using the formula:

PV = PMT x [1 - (1 + r)^-n] / r

Where: PMT = the amount of each payment r = the annual interest rate n = the number of payments

a. $600 per year for 12 years at 8% PV = $600 x [1 - (1 + 0.08)^-12] / 0.08 = $5,591.71

b. $300 per year for 6 years at 4% PV = $300 x [1 - (1 + 0.04)^-6] / 0.04 = $1,593.84

c. $500 per year for 8 years at 14%:

Using the formula for future value of an annuity:

FV = PMT x [(1 + r)^n - 1] / r

where PMT is the annual payment, r is the annual interest rate, and n is the number of years.

Plugging in the values given:

FV = 500 x [(1 + 0.14)^8 - 1] / 0.14 FV = $5,773.91 (rounded to the nearest cent)

Therefore, the future value of the annuity is $5,773.91 after 8 years.

$250 per year for 4 years at 7%:

FV = 250 x [(1 + 0.07)^4 - 1] / 0.07 FV = $1,075.65

Therefore, the future value of the annuity is $1,075.65 after 4 years.

$700 per year for 4 years at 0%:

FV = 700 x [(1 + 0)^4 - 1] / 0 FV = $2,800

Enter information on chart:

Future Value Present Value Interest Rate Interest Rate # of Periods # of Periods Starting Value Lump Sum in the Future Future Lump Sum $ Present Value SoRequired Interest Rates Present Value in savings Future Value needed at retirement Additional funds Number of Periods years Required Interest Rate #NUM!Future Value of an Annuity a Present Value of an Annuity Interest Rate Interest Rate # of Periods # of Periods Payments (per period) Payment per period Future Value Present Value $0.00 b) Future Value of an Annuity b) Present Value of an Annuity Interest Rate Interest Rate # of Periods # of Periods Payments (per period) Payment per period Future Value Present Value $0.00 Future Value of an Annuity c) Present Value of an Annuity Interest Rate Interest Rate # of Periods # of Periods Payments (per period) Payment per period Future Value $ Present Value $0.00