Question

Stella invested $42,000 in an account paying an interest rate of 4 7/8% compounded quarterly. Chloe invested $42,000 in an account paying an interest rate of 4 1/2% compounded annually. To the nearest dollar, how much money would Stella have in her account when Chloe's money has tripled in value?

Answer 1

Answer: Stella would have $15036 more than Chloe.

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

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

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

Considering Chloe's investment,

P = 42000

r = 4.5% = 4.5/100 = 0.045

n = 1 because it was compounded once in a year.

A = 42000 × 3 = 126000

Therefore,.

126000 = 42000(1 + 0.045/1)^1 × t

126000/42000 = (1.045)^t

3 = (1.045)^t

Taking log of both side,

Log3 = tlog1.045

0.4771 = 0.019t

t = 0.4771/0.019

t = 25.11

Approximately 25 years

Considering Stella's investment,

t = 25

P = 42000

r = 4.875% = 4.875/100 = 0.04875

n = 4 because it was compounded 4 times in a year.

Therefore,

A = 42000(1 + 0.04875/4)^4× 25

A = 42000(1 + 0.0121875)^100

A = 42000(1.0121875)^100

A = 42000 × 3.358

A = $141036

The difference in amount would be

141036 - 126000 = $15036