Question

Suppose that $2000 is loaned at a rate of 12.5% compounded semiannually. Assuming that no payments are made, find the amount owed after 6 years. Do not round any intermediate computations, and round your answer to the nearest cent.

Answer 1

The formula for annual compound interest, including principal sum, is:

`A=P(1+(r)/(n))^(nt)`

where

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years the money is invested or borrowed for

Here, we have to find semi-annually

`\begin{gathered} P=2000 \\ r=12.5\%=(12.5)/(100)=0.125 \\ n=2\text{ for semi-annually} \\ t=6 \end{gathered}`

Therefore,

`\begin{gathered} A=2000(1+(0.125)/(2))^(2*6)=2000(1+0.0625)^(12) \\ A=2000(1.0625)^(12)=4139.77998355904\approx4139.78 \\ \therefore A=\text{ \$4139.78} \end{gathered}`

Hence, the amount owed after 6 years is $4139.78.