nent

Compounding More Frequent than

Annually

$4\mathrm{.}12.$ How much will $$8,000$ be worth in $8$ years with $6\mathrm{.}75\%$ interest compounded continuously?

$4\mathrm{.}13.$ How much money must you deposit now to have $$6,000$ in ten years at $6\mathrm{.}5\%$ compounded continuously?

$4\mathrm{.}14.$ How much money will you have in seven years if you deposit $$7,000$ in the bank at $8\mathrm{.}5\%$ interest compounded daily?

$4\mathrm{.}15.$ How long will it take money to triple with continuous compounding at $8\%$ interest?

$4\mathrm{.}16.$ Republic Finance offers money at $2\mathrm{.}32\%$ per month compounded monthly.

$($a$)$ What is the nominal interest rate?

$($b$)$ What is the effective annual interest rate?

$($c$)$ How many years will it take an investment to triple if interest is compounded monthly?

$($d$)$ How many years will it take an investment to quadruple if the nominal rate is compounded continuously?

$4\mathrm{.}17.$ Suppose your savings account pays $6\%$ interest compounded monthly. If you deposit $$18,000$ for four years, how much will you have?

$4\mathrm{.}18.$ If you invest $$25,000$ today at a $7\mathrm{.}5\%$ interest compounded weekly, what will be your ending value after $15$ years?

$4\mathrm{.}19.$ What will be the amount accumulated by each of these present investments?

$($a$)$ $$12,250$ in $15$ years at $8\mathrm{.}5\%$ compounded quarterly.

$($b$)$ $$15,750$ in $12$ years at $8\mathrm{.}32\%$ compounded weekly.

$($c$)$ $$25,500$ in $10$ years at $7\mathrm{.}5\%$ compounded monthly,

$4\mathrm{.}20.$ How many years will it take an investment to double if the interest rate is $8\mathrm{.}4\%$ compounded at the given intervals?

$($a$)$ Quarterly

$($b$)$ Monthly

$($c$)$ Continuously

$4\mathrm{.}21.$ A series of equal quarterly payments of $$25,000$ for $10$ years is equivalent to what future worth amount at an interest rate of $8\mathrm{.}4\%$ compounded at the given intervals?

$($a$)$ Quarterly

$($b$)$ Monthly

$($c$)$ Continuously