Question

Nicholas earned $2,000.00 working over the summer and wants to put the money into a savings account. A savings account at bank A earns 5% simple interest and a savings account at bank B earns 4% interest compounded quarterly. If Nicholas plans to deposit the $2,000.00 and leave it in the account for 4 years, at which bank would he earn more interest? A. The interest earned cannot be calculated from the given information. B. The interest earned at both banks will be the same. C. bank A D. bank B

Answer 1

Choice C
==> Bank A

Explanation:

Principal P = $2000

Bank A calculation

Simple Interest at 5% for 4 years = Prt = 2000 x 5/100 x 4 = $400

Bank B Calculation

At 4% interest compounded quarterly, the accrued value(Principal + Interest) is given by the formula:

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

where

P = principal

r = annual interest rate as percentage

n = number of compounding per year

t = number of years

We have r = 4/ 100 = 0.04

n = 4 since interest is computed quarterly or 4 times a year

t = 4 years

`A = 2000 ( 1 + 0.04/4)^((4) \cdot (4))\\\\A = 2000 (1.01)^(16) = \$2,345.16\\\\\text{Interest } = 2345.16 - 2000 = $345.16`

Since interest earned at bank A (400) > interest earned at bank B(345.16), the answer would be C. ==> Bank A