A customer deposits $2000 in a savings account that pays 5.2% interest compounded quarterly. How much money will the customer have in the account after 2 yr? After 5 yr?

Question

asked May 14, 2019 189k views

1 Answer

Maddy D · Answer 1 · 2019-05-19T10:48:17+0000

To solve this we are going to use the compound interest formula:

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

where

is the amount after

years

is the initial amount

is the interest rate in decimal form

is the number of times the interest is compounded per year

is the time in years.

First, we are going to convert the interest rate to decimal form by divide the rate by 100%:

(5.2)/(100) =0.052

Next, we are going to find

. Since the interest is compounded quarterly, it is compounded 4 times per year, so.

n=4

1. For our problem we know that
t=2

and

. We also know for our previous calculations that
r=0.052

and

. So lets replace those values in our compound interest formula to find

:

$A=2000(1+ (0.052)/(4) )^{(2)(4)$

A=2000(1+ (0.052)/(4))^(8)

We can conclude that after 2 years the customer will have $2,217.71 in his account.

2. We know for our problem that this time
t=5

, the initial investment remains the same, so
p=2000

, and we also know for our previous calculations that
r=0.052

and

. So lets replace those values in our formula one more time:

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

$A=2000(1+ (0.052)/(4) )^{(4)(5)$

A=2000(1+ (0.052)/(4) )^(20)

We can conclude that after 5 years the customer will have $2,589.52 in his account.