Question

Bank A offers a saving account with a 6% APR compounded semiannually. Bank B offers the same rate but compounds monthly. If $1000.00 is invested in both banks, find the difference in interest earned at the end of the year.

Answer 1

$0.78

Explanation:

Here we have to use the formulas.

Compound interest calculate semiannually

A = P(1 + r/2)^2n

Where P = Principal

R = Rate and n = number of years

Here n = 1, r = 6% = 0.06

A = 1000(1 + 0.06/2)^2(1)

= 1000(1 +0.03)^2

= 1000 (1.03)^2

= 1000(1.0609)

A = 1060.9

Compound interest = 1060.9 - 1000

= $60.90

Compound interest calculated monthly

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

Here is n is the number of times the interested compounded per year, n = 12 and t = number of years

A= 1000(1 + 0.06/12)^12(1)

A= 1000(1 + 0.005)^12

A= 1000(1.005)^12

A= $1061.68

Compound interest calculated monthly (after 1 year) = 1061.68 - 1000

=$61.68

The difference in interest earned at the end of the year = $61.68 - $60.90

= $0.78

Thank you.