Question

Compute the compound amount and the interest on a loan of ​$10800 compounded annually for four years at 10​%. Use the​ $1.00 future value table or the future value and compound interest formula.

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10800\\ r=rate\to 10\%\to (10)/(100)\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}`

`A = 10800\left(1+(0.10)/(1)\right)^(1\cdot 4) \implies \boxed{A = 15812.28} ~\hfill \underset{ earned~interest }{\stackrel{ 15812~~ - ~~10800 }{\boxed{5012}}}`

Answer 2

$5,149.44

Explanation:

To calculate the compound amount and interest on a loan of ​$10800 compounded annually for four years at 10%, we can use the formula:

A = P(1 + r)^t

where A is the compound amount, P is the principal (the initial loan amount), r is the interest rate (as a decimal), and t is the number of years.

In this case, P = $10800, r = 0.10 (10% as a decimal), and t = 4. Substituting these values into the formula, we get:

A = $10800(1 + 0.10)^4

A = $10800(1.10)^4

A = $15,949.44

Therefore, the compound amount after four years is $15,949.44.

To calculate the interest, we can subtract the principal from the compound amount:

Interest = $15,949.44 - $10,800

Interest = $5,149.44

Therefore, the interest on the loan is $5,149.44.