Question

Find the future value and interest earned if $8906.54 is invested for 9 years at 6% compounded semianually

Answer 1

Answer:

Future Value is $15162.79

Interest is $6256.25

Step-by-step explanation:

Future value of a principal amount is the value after a given amount of time at an assumed rate of growth. Compound interest considers the return on investment (or interest) to be reinvested and provides return as well.

Future value of principal value (considering compounding) and interest can be determined by below formulas

$FV=P(1+\frac{r}{n})^{nt}$

$I=FV-P$

where FV is the future value, P is principal, r is the rate of interest, n is the number of times interest is compounded per unit time, t is the time of investment and I is interest

$P= 8906.54$

$r=6% annually$

$n=2$

$t=9$

$FV=P(1+\frac{r}{n})^{nt}$

$FV=8906.54(1+\frac{0.06}{2})^{2*9}$

$FV=8906.54(1.03)^{18}$

$FV= 15162.79$

$I=FV-P$

$I=15162.79-8906.54$

$I= 6256.25$

Answer 2

The future value and interest earned are $15,162.78 and $6,256.78 respectively.

Compound interest

This is expressed according to the formula;

$A =P(1+r/n)^{nt}$

Given the following

• P = $8906.54
• r = 6% = 0.06
• t = 9 years

Substitute into the formula

$A =8906.54(1+0.06/2)^{2(9)}\\ A = \ 15,162.78$

The interest is expressed as:

I =  15,162.78 - 8906.54

I = $6,256.78

Hence the future value and interest earned are $15,162.78 and $6,256.78 respectively.

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