Question

Emilia opened a savings account and deposited $400.00 as principal. The account earns 4% interest, compounded quarterly. What is the balance after 4 years? nt Use the formula A = P where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.

Answer 1

To calculate the final amount of the acount that compounds quarterly you have to use the following formula:

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

Where

A is the accrued amount

P is the principal amount

r is the interest rate, expressed as a decimal value

t is the time period

n is the number of compound periods per time unit. This savings account compounds quarterly, this means, 4 times per year

P=$400.00

r=4/100=0.04

t= 4 years

n=4*4=16

`\begin{gathered} A=400(1+(0.04)/(16))^(16\cdot4) \\ A=469.31 \end{gathered}`

The amount at the end of the 4 year period will be $469.31