Taylor deposits $150 in each of two savings accounts. Both have an annual interest rate of 4%. No additional deposits or withdrawals are made. One account earns simple interest, and the other account earns interest compounded annually. How much more does the compound interest account earn than the simple interest account after 20 years?

Answer: $59

Step-by-step explanation:

Considering the account that earns simple interest, we would apply the formula for determining simple interest which is expressed as

I = PRT/100

Where

I represents interest paid on the amount of money deposited.

P represents the principal or amount of money deposited.

R represents interest rate on the deposit.

T represents the duration of the deposit in years.

From the information given,

P = $150

R = 4%

T = 20 years

Therefore,

I = (150 * 4 * 20) / 100

I = $120

Considering the account that earns compound interest, 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

From the information given,

P = $150

r = 4% = 4/100 = 0.04

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

t = 20 years

Therefore,

A = 150 (1 + 0.04/1) ^1 * 20

A = 150 (1.04) ^20

A = $329

The interest is

329 - 150 = $179

The additional interest that the compound interest account earn than the simple interest account after 20 years is

179 - 120 = $59