Question

Benjamin receives an annual bonus of $1000. He plans to deposit this bonus intoone of the following savings account for 3 years.Bank A5% Simple InterestBank B5% Interest Compounded AnnuallyWhich of the following statements is true?A. After 3 years, Bank A will pay Benjamin $7.63 more than Bank B.B. After 3 years, Bank B will pay Benjamin $7.63 more than Bank A.C. After 3 years, Bank A will pay Benjamin $23.13 more than Bank B.D. After 3 years, Bank B will pay Benjamin $23.13 more than Bank A.

Answer 1

Simple interest formula:

A = P(1 + rt)

Compound interest formula:

`^{}A=P(1+r)^t`

where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), and t is time in years.

Substituting with P = 1000, r = 0.05, and t = 3 into both cases, we get:

`\begin{gathered} A_A=1000\cdot(1+0.05\cdot3) \\ A_A=1000\cdot(1.15) \\ A_A=1150 \\ A_B=1000\cdot(1+0.05)^3 \\ A_B=1000\cdot(1.05)^3 \\ A_B=1000\cdot1.15763 \\ A_B=1157.63 \end{gathered}`

B. After 3 years, Bank B will pay Benjamin $7.63 (= $1157.63 - $1150) more than Bank A.