Question

Katherine invested $86,000 in an account paying an interest rate of 52%

compounded daily. Michael invested $86,000 in an account paying an interest rate of
5% compounded continuously. After 13 years, how much more money would
Katherine have in her account than Michael, to the nearest dollar?

Answer 1

Answer: $4,331‬

Explanation:

I will assume that the question meant 5.2% not 52% as this is quite excessive.

Katherine after 13 years.

Convert the variables;

n = 13 years = 13 * 365 = ‭4,745‬ days

r = 5.2% = 5.2/365 = 5.2/365%

Future value = P * ( 1 + r)^n

= 86,000 * (1 + 5.2/365%)⁴⁷⁴⁵

= $169,068

Michael after 13 years;

If compounded continuously, the formula is;

Future value = Pe^rt

= 86,000 * e⁰.⁰⁵ ˣ ¹³

= $164,737

Difference = 169,068 - 164,737

= $4,331‬