$4.$ How many days will it take for a sum of $$1500$ to earn $$30$ interest if it is deposited in a

account paying $6\%$ per year simple interest? $(365$ days per year.$)$

Answer: $122$ days

$5.$ A bank deposit paying simple interest grew from an initial sum of $$1800$ to a

sum of $$1881$ in nine months. Find the annual interest rate.

Answer: $6\%$

$6.$ Consider an investment of $$900$ made for two years at a simple interest rate of

$7\mathrm{.}5\%$ per year.

$($a$)$ Find the amount of simple interest earned.

Answer: $$135$

$($b$)$ Find the accumulated amount.

Answer: $$1035$

$7.$ What is the interest earned on $$1$ million, invested at $18\%$ per year for $4$ years,

and compounded annually?

Answer: $$938,777\mathrm{.}76$

$8.$ Find the difference between the compound interest and the simple interest if

$$250$ is invested at $7\mathrm{.}5\%$ per year for $3$ years.

Answer: $$4\mathrm{.}32$ more with compound interest

$9.$ What is the future value of $$1250,$ invested at $9\mathrm{.}5\%$ per year for $5$ years, if interest is

Mathematics of Finance

$41$

compounded semiannually?

Answer: $$1988\mathrm{.}16$

$10.$ What is the future value of $$4500,$ invested at $15\%$ per year for $20$ years, if interest is

compounded quarterly?

Answer: $$85,558\mathrm{.}06$

$11.$ What is the future value of $$20,000,$ invested at $6\mathrm{.}5\%$ per year for $7$ years, if interest

is compounded monthly?

Answer: $$31,484\mathrm{.}79$

$12.$ What is the future value of $$1$ million, invested at $18\%$ per year for $4$ years, if interest

is compounded daily?

Answer: $$2,054,069$

$13.$ What is the present value of an investment earning $12\%$ per year compounded

monthly if it is worth $$25,000$ in two years?

Answer: $$19,689\mathrm{.}15$

$14.$ What is the annual yield of an interest rate of $9\mathrm{.}5\%$ per year compounded quarterly?

Answer: $9\mathrm{.}84\%$

$15.$ What is the total amount of interest paid on a $$2,500$ loan for three years at $18\%$ per

year compounded annually?

Answer: $$1607\mathrm{.}58$

$16.$ What is the total amount that must be repaid on a $$5,000,$ two$-$year loan at $12\%$ per

year, compounded monthly?

Answer: $$6348\mathrm{.}67$

$17.$ Find the effective rate of interest corresponding to a nominal rate of $15\mathrm{.}5\%$ per

year compounded monthly. $($Round to the nearest hundredth of one percent.$)$

Answer: $16\mathrm{.}65\%$ per year

$18.$ Find the effective rate of interest corresponding to a nominal rate of $6\mathrm{.}5\%$ per year

compounded monthly. $($Round to the nearest tenth of one percent.$)$

Answer: $6\mathrm{.}7\%$ per year

$19.$ Find the time, in years, that it takes for an investment to double in value when interest

is compounded daily at a rate of $7\%$ per year. $($Round to the nearest tenth of a year.$)$

Answer: $9\mathrm{.}9$ years

$20.$ Find the time, in years, that it will take for an investment to triple in value when

interest is compounded daily at a rate of $9\%$ per year. $($Round to the nearest tenth of

a year.$)$

Chapter $4$

$42$

Answer: $12\mathrm{.}2$ years

$21.$ How much interest is earned on $$2000$ invested for two years at $9\%$ per year

compounded monthly?

Answer: $$392\mathrm{.}83$

$22.$ What is the interest earned on $$10,000$ invested for five years at $9\%$ per year

compounded quarterly?

Answer: $$5605\mathrm{.}09$

$23.$ A father wants to be able to provide his newborn baby with a college education.

To do this, the father estimates that he will need $$120,000$ when his child turns

$18.$ How much money should the father invest in an account that pays $7\%$

interest per year compounded daily so that the account is worth $$120,000$ in $18$

years?

Answer: $$34,042\mathrm{.}60$