Question

Jane has two savings accounts, Account S and Account C. Both accounts are opened with an initial deposit of $300 and an annual interest rate of 3.5%. No additional deposits are made, and no withdrawals are made. Account S earns simple interest, and Account C earns interest compounded annually. Which account will earn more interest after 10 years? How much more?

Answer 1

Explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the investment.

P represents the principal or amount invested.

R represents interest rate

T represents the duration of the investment.

Considering account S,

P = $300

R = 3.5%

T = 10 years

I = (300 × 3.5 × 10)/100 = $105

Considering account C, 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 = 300

r = 3.5% = 3.5/100 = 0.035

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

t = 10 years

Therefore,

A = 300(1 + 0.035/1)^1 × 10

A = 300(1.035)^10

A = $423

Interest = 423 - 300 = $123

Account C will earn more. The amount by which it will earn more that account S is

123 - 105 = $18