A friend was left $50,000 by his uncle. He has decided to put it into a savings account for the next year or so. He finds there are varying interest rates at savings institutions: 2.25% compounded every two months, 2.30% compounded quarterly, and 2.20% compounded continuously. He wishes to select the savings institution that will give him the highest return on his money.
What interest rate should he select?

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hyderali230 hyderali230 · Answer 1 · 2020-02-14T08:13:36+01:00

Answer:

He should select 2.30% Compounded every Quarterly because it gives the highest return of $1,159.96.

Explanation:

Principal Amount = P = $50,000

t = 1 year

Using following formula compare the interest rates

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

Savings account with interest rate of

2.25% Compounded every two months

r = 2.25%

n = 12/2 = 6

A = $5,000 ( 1+ (0.0225/6))^6x1

A = $50,000 ( 1+ (0.00375))^6

A = $51,135,59

2.30% Compounded every Quarterly

r = 2.30%

n = 12/3 = 4

A = $5,000 ( 1+ (0.023/4))^4x1

A = $50,000 ( 1+ 0.00575)^4

A = $51,159,96

2.20% Compounded Continuously

A = P x [tex]e^{rt}[/tex]

A = $50,000 x [tex]e^{0.022}[/tex]

A = $50,000 x 1.0222438

A = 51,112.19

So, he should select 2.30% Compounded every Quarterly because it gives the highest return.