Question

Find the future value of the account pays (a)simple interest and (b)compounded interest annually. $2000 at 9% for 7 years.

Answer 1

Answer:

• (a)The future value at simple interest is $3,260.

,

• (b)The future value at compounded interest is $3,656.08

Explanation:

• Principal, P = $2,000

,

• Rate, r = 9%

,

• Time, t = 7 years

(a)Future value at simple interes

$\begin{gathered} F.V=Principal+Interest \\ =P+\frac{PRT}{100} \\ =2000+\frac{2000\times9\times7}{100} \\ =2000+1260 \\ =\ 3,260 \end{gathered}$

The future value at simple interest is $3,260.

(b)Future value at compounded interest

$Future\;Value,A(t)=P(1+r)^t$

Substitute the values of P, r and t:

$\begin{gathered} A(7)=2000\left(1+\frac{9}{100}\right)^7 \\ =2000(1+0.09)^7 \\ =2000(1.09)^7 \\ =\ 3656.08 \end{gathered}$

The future value at compounded interest is $3,656.08