Question

Kendrick opened a savings account and deposited $3,000.00 as principal. The account earns 6% interest, compounded quarterly. How much interest will he earn after 7 years?

Answer 1

$1551.67

Explanation:

At Compound Interest, the Amount, A accrued by a Principal P for a period of t years compounded n times in a year at a rate of r is derived using the formula:

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

P=$3,000.00

r=6% = 0.06

n=4 (Since it is compounded quarterly)

t= 7 years

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

`A=3000(1+(0.06)/(4))^(4 X 7)\\ =3000(1+0.015)^(28)\\ =3000(1.015)^(28)\\ =4551.67`

The Interest earned after 7 years will be:

Interest= Amount - Principal

=4551.67 - 3000

=$1551.67

Answer 2

Amount of interest after 7 years = $12335.06

Explanation:

First total number of quarters in 7yrs is calculated

a year has four quarters, hence 7yrs will have = 4 x 7 = 28 quarters

Using the compound interest expression

Amount after 7 yrs = P(1+r%)²⁸

A = 3000 (1+0.06)²⁸ = $15335.06

Hence amount of interest after 7 years = 15335.06 - 3000 = 12335.06