Question

When their child was born, Elaine and Mike Porter deposited $5,000 in a savings account at Tennessee Trust. The money earns interest at 6% compounded quarterly. Considering that they make no other deposits or withdrawals, how much will the account be worth in two years

Answer 1

The account be worth in two years be $5632.5 .

Explanation:

Formula for compounded quarterly

`Amount = P (1 + (r)/(4))^(4t)`

Where P is the principle , r is the rate of interest in the decimal form and t is the time.

As given

Elaine and Mike Porter deposited $5,000 in a savings account at Tennessee Trust.

The money earns interest at 6%

P = $5000

6% is written in the decimal form.

`= (6)/(100)`

= 0.06

r = 0.06

t = 2 years

Put all the value in the formula

`Amount = 5000 (1 + (0.06)/(4))^(4* 2)`

`Amount = 5000 (1 + (0.06)/(4))^(8)`

`Amount = 5000 (1 + 0.015)^(8)`

`Amount = 5000 (1.015)^(8)`

`Amount = 5000* 1.1265\ (Approx)`

Amount = $5632.5 (Approx)

Therefore the account be worth in two years be $5632.5 .

Answer 2

Amount in compound interest = p(1 + r/t)^nt where p is the initial deposit, r = rate, t = number of compunding in a period and n = period.

Here, Amount after 2 years = 5,000(1 + (6/100)/4)^(2 x 4) = 5,000(1 + 0.06/4)^8 = 5,000(1 + 0.015)^8 = 5,000(1.015)^8 = 5,000(1.126493) = $5,632.46