$12$K MATH $90---$ Mathematics of Finance

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Question $1$

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The notion behind the time value of money is the underlying principle that

a$.$

a dollar is not worth much

b$.$

a dollar today is worth more than a dollar tomorrow

c$.$

a dollar today is always less than two dollars in the future

d$.$

a dollar tomorrow is equal in value to a dollar tomorrow

e$.$

a dollar tomorrow is worth more than a dollar today

Question $2$

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Which is a plausible explanation as to why Jim would prefer to receive $ $1000$ from today rather than $ $1050$ in one year?

a$.$

The money would be paid by Jim$$s father. Jim is sure that his father will make either payment.

b$.$

Jim recently received a lot of money from his grandfather. He is currently not so sure of how he will use all that money.

c$.$

Jim wants to spend the money on the latest Yeezy sneakers. He does not know whether the shoes will be available $($or fashionable$)$ by next year.

d$.$

Jim is not a very savvy crypto investor. He would probably use the money to buy Treasury securities $-$ earning $3\%$ a year.

e$.$

For the last several years, the rate of inflation has averaged around $3\%$ per year.

Question $3$

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If the compounding frequency is monthly, then m $($the number of compounding periods per year$)$ is:

a$.$

$4$

b$.$

$12$

c$.$

$1$

d$.$

$365$

e$.$

$2$

Question $4$

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You want to determine the future value of $$18100$ after $10$ years at $9\mathrm{.}72\%$ per annum compounded monthly. Find i $($periodic rate$)$

a$.$

$9\mathrm{.}72\%$

b$.$

$4\mathrm{.}86\%$

c$.$

$2\mathrm{.}43\%$

d$.$

$0\mathrm{.}0081\%$

e$.$

$0\mathrm{.}81\%$

Question $5$

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You wish to calculate the present value of $$12500\mathrm{.}00$ due in two years and nine months if interest is $7\mathrm{.}8\%$ p$.$a$.$ compounded every two months. Find n $($the number of compounding periods$)$

a$.$

$16\mathrm{.}5$

b$.$

$39$

c$.$

$8\mathrm{.}25$

d$.$

$65$

e$.$

$11$

Question $6$

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Calculate the effective rate of interest for the first year, if the rate of interest is $18\%$ p$.$a$.$ compounded quarterly? $($rounding the answer to $6$ significant decimal figures$)$

a$.$

$0\mathrm{.}195618$

b$.$

$0\mathrm{.}188100$

c$.$

$0\mathrm{.}192519$

d$.$

$0\mathrm{.}203251$

e$.$

$0\mathrm{.}180593$

Question $7$

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You are trying to calculate how long it will take $ $8000$ invested at $8\%$ p$.$a$.$ compounded quarterly to double. Applying the tools that you have learned in this class you initially find n $($the number of periodic periods$).$ This answer No will initially be in terms of

a$.$

years

b$.$

days

c$.$

quarters

d$.$

months

e$.$

half$-$years

Question $8$

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What is the discounted value of deposits of $ $180$ made at the end of each month for fourteen years if interest is $4\mathrm{.}5\%$ compounded monthly?

a$.$

$ $27805\mathrm{.}45$

b$.$

$ $20605\mathrm{.}45$

c$.$

$ $26005\mathrm{.}45$

d$.$

$ $24205\mathrm{.}45$

e$.$

$ $22405\mathrm{.}45$

Question $9$

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Fred bought a vacation property for $ $17490$ down and monthly mortgage payments of $$1224\mathrm{.}51$ at the end of each month for six years. Interest is $8\mathrm{.}4\%$ compounded monthly. What is the purchase price of the property?

a$.$

$ $86557\mathrm{.}43$

b$.$

$ $83059\mathrm{.}43$

c$.$

$ $88306\mathrm{.}43$

d$.$

$ $90055\mathrm{.}43$

e$.$

$ $85682\mathrm{.}93$

Question $10$

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Joanna plans to pay off a debt by payments of $ $1400$ one year from now, $ $1300$ eighteen months from now, and $ $1800$ thirty months from now. What single payment now would settle the debt if money is worth $8\%$ p$.$a$.$ compounded quarterly?

a$.$

$ $3924\mathrm{.}37$

b$.$

$ $4157\mathrm{.}30$

c$.$

$ $4046\mathrm{.}09$

d$.$

$ $4500\mathrm{.}00$

e$.$

$ $3836\mathrm{.}46$

Question $11$

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$1$ Bitcoin was at $ $900$ on January $1,2017.$ On January $1,2021,$ the price of $1$ Bitcoin was $ $32000$ a coin. Calculate the price appreciation of cryptocurrency as percent per year, compounded annually. $($This is not investment advice$)$

a$.$

$45\mathrm{.}18\%$

b$.$

$144\mathrm{.}19\%$

c$.$

$14\mathrm{.}42\%$

d$.$

$18\mathrm{.}94\%$

e$.$

$234\mathrm{.}92\%$

Question $12$

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Galaxy Company has added a crypto fund. The high$-$risk fund will earn a significant risk$-$reward return rate of $24\%$ per year, compounded monthly. Find how long it will take $ $9000$ invested in this fund to become $ $18000.$

a$.$

$3\mathrm{.}19$ years

b$.$

$2\mathrm{.}91$ years

c$.$

$1\mathrm{.}93$ years

d$.$

$2\mathrm{.}47$ years

e$.$

$2\mathrm{.}67$ years

Question $13$

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Galaxy Company has added a crypto fund. The high$-$risk fund will earn a significant risk$-$reward return rate of $24\%$ per year, compounded monthly. Find how long it will take $ $12000$ invested in this fund to quadruple $($x $4).$

a$.$

$5\mathrm{.}83$ years

b$.$

$5\mathrm{.}74$ years

c$.$

$3\mathrm{.}86$ years

d$.$

$4\mathrm{.}94$ years

e$.$

$6\mathrm{.}38$ years

Question $14$

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Galaxy Company has added a crypto fund. The high$-$risk fund will earn a significant risk$-$reward return rate of $24\%$ per year, compounded monthly. Find how long it will take $ $12000$ invested in this fund to grow eightfold $($x $8).$

a$.$

$5\mathrm{.}83$ years

b$.$

$5\mathrm{.}79$ years

c$.$

$8\mathrm{.}75$ years

d$.$

$9\mathrm{.}57$ years

e$.$

$7\mathrm{.}41$ years

Question $15$

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On September $1,2010,$ you put $ $17000$ in a money market fund. On March $1,2015,$ you deposit another $ $16000$ and on January $1,2018,$ you added another $ $11000.$ This fund pays interest at the annual rate of $7\mathrm{.}2\%,$ compounded monthly. Find the future value of the fund on March $1,2015,$ immediately after the second deposit.

a$.$

$ $39752\mathrm{.}20$

b$.$

$ $38917\mathrm{.}39$

c$.$

$ $38498\mathrm{.}72$

d$.$

$ $39482\mathrm{.}25$

e$.$

$ $39582\mathrm{.}04$

Question $16$

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On September $1,2010,$ you decided to put $ $17000$ in a money market fund. On March $1,2015,$ you deposit another $ $16000$ and on January $1,2018,$ you added another $ $11000.$ This fund pays interest at the annual rate of $7\mathrm{.}2\%,$ compounded monthly. Find the future value of the fund on January