Question

Solve the problem. Round to the nearest cent.

Stan’s savings account has a balance of $1986. After 23 years, what will the amount of interest be at 4% compounded annually?
a.
$2908.93
c.
$2913.93
b.
$2899.93
d.
$794.40

Answer 1

1986*1.04^(23) = 4894.93

4894.93-1986 = 2908.93

Answer is A

Answer 2

Answer:

a.  $2908.93

Step-by-step explanation:

We have been given that Stan’s savings account has a balance of $1986. The amount of interest be at 4% compounded annually.

To find the final amount after 23 years we will use compound interest formula.

$A=P(1+\frac{r}{n})^{nT}$, where,

A = Final amount,

P= Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest in compounded per year,

t = Time in years.

Let us convert our given rate in decimal form.

$4\%=\frac{4}{100}=0.04$

Upon substituting our given values in above formula we will get,

$A=\ 1986(1+\frac{0.04}{1})^{1*23}$

$A=\ 1986(1+0.04)^{23}$

$A=\ 1986(1.04)^{23}$

$A=\ 1986*2.4647155431651442$

$A=\ 4894.9250687259763812$

To find the amount of interest we will subtract principal amount from final amount.

$\text{Amount of interest}=\ 4894.9250687259763812-\ 1986$

$\text{Amount of interest}=\ 2908.925068725976\approx 2908.93$

Therefore, the amount of interest after 23 years will be $2908.93 and option a is the correct choice.