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Joe is taking out a loan for
$1,500 with an annual compound interest rate of
15% for 3 years. Joe will not make any additional deposits or withdrawals. What will be the total balance paid at the end of 3 years?

Joe is taking out a loan for $\$ 1,500$ with an annual compound interest rate of $15 \%$ for $3$ years. Joe will not make any additional deposits or withdrawals. What will be the total balance paid at the end of $3$ years?

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Finance problems

Full solution

Q. Joe is taking out a loan for

\$ 1,500

with an annual compound interest rate of

15 \%

for

3

years. Joe will not make any additional deposits or withdrawals. What will be the total balance paid at the end of

3

years?

Identify Variables: Identify the variables for the compound interest formula. $\newline$ Principal amount $P$ = $\$1,500$ $\newline$ Annual interest rate $r$ = $15\%$ or $0.15$ (as a decimal) $\newline$ Number of years $t$ = $3$ $\newline$ Compound frequency $n$ = $1$ (since no specific compounding frequency is mentioned, we assume it is compounded annually)
Use Formula: Use the compound interest formula to calculate the total balance at the end of $3$ years. $\newline$ The compound interest formula is $A = P(1 + r/n)^{(nt)}$ , where $A$ is the amount of money accumulated after $n$ years, including interest. $\newline$ Substitute the given values into the formula: $\newline$ $A = 1500(1 + 0.15/1)^{(1*3)}$
Calculate Total Balance: Calculate the total balance using the formula. $\newline$ $A = 1500(1 + 0.15)^{3}$ $\newline$ $A = 1500(1.15)^{3}$ $\newline$ $A = 1500 \times 1.15^3$ $\newline$ $A = 1500 \times 1.520875$ $\newline$ $A = 2281.3125$
Check Calculation: Check the calculation for any mathematical errors. $\newline$ Re-evaluate the exponent: $\newline$ $1.15^3 = 1.520875$ (correct) $\newline$ Multiply by the principal amount: $\newline$ $1500 \times 1.520875 = 2281.3125$ (correct)

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