Investment

Question

Suppose you have $13,000 to invest. Which of the two rates would yield the larger amount in 5 years: 10% compounded daily or 9.90% compounded continuously? Which of the two rates would yield the larger amount in 5 years?

Answer 1

Apply compound interest formula:

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

 

where,

A = amount of money accumulated after n years, including interest.

P = principal amount (the initial amount you deposit) = $13000

r = annual rate of interest as a decimal = 10% = 0.1

n = number of times the interest is compounded per year= 365 (for daily compounding)

t = number of years the amount is invested = 5

So, for daily compounding:
A = 13000(1+0.1/365)^(365*5) = $ 21431.91

 

For continuous compounding

A = P*e^rt

A = 13000 *e^(0.099*5)

A = $ 21326.48

 

So, clearly 10% compounded daily would yield a larger amount.