Question

Stan's savings account has a balance of $4706. after 4 years, what will the amount of interest be at 4% compounded quarterly?

Answer 1

Answer: b. $812.16

Step-by-step explanation:

The concept of compound interest is that interest is added back to the principal sum so that interest is gained on that already-accumulated interest during the next compounding period.  

Interest can be compounded on any given frequency schedule, from continuous to daily to annually. When incorporating multiple compounds per period (monthly compounding or quarterly compounding, etc), the general formula looks like this:

$\boxed{A = P(1 +\frac{r}{n})^{n*t}}$

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 = number of times interest is compounded per unit "t"  

t = the time the money is invested or borrowed for

Using the data provided in the question  

P = $4706

r = 4/100 = 0.04

n = 4 (compounded quarterly)  

t = 4 years

$A = 4706(1 +\frac{0.04}{4})^{4*4}$  

A = $4706(1 + 0.04/4)¹⁶

A = $4706(1 + 0.01)¹⁶

A = $4706(1.01)¹⁶

A = $4706(1.1725787) = $5518.16

This formula gives the combined principal amount and its compound interest, so subtract the principal amount to get just the compound interest.

$5518.16 - $4706 = $812.16

Answer: b. $812.16

$\textit{\textbf{Spymore}}$