Question

If you put $100,000 in to a bank account earning 3% interest, how much will you have in 5 years if the 3% is an annually compounded APR? What if it is a semiannually compounded APR? What if it is a monthly compounded APR? What if it is a continuously compounded APR?

Answer 1

a)
FV = PV * (1+r)^n

= $100,000 * (1 + 3%)^5

= $100,000 * 1.15927407

= $115,927.41

Amount at the end of 5 years = $115,927.41

b)
FV = PV * (1+r/m)^(m*n)

= $100,000 * (1 + 3%/2)^(5 * 2)

= $100,000 * 1.015^10

= $100,000 * 1.1605408

= $116,054.08

Amount at the end of 5 years = $116,054.08

c)
FV = PV * (1+r/m)^(m*n)

= $100,000 * (1 + 3%/12)^(5 * 12)

= $100,000 * 1.0025^60

= $100,000 * 1.161616782

= $116,161.68

Amount at the end of 5 years = $116,161.68

d)

FV = PV * e^(r*t)

= $100,000 * e^(0.03 * 5)

= $100,000 * 1.161834243

= $116,183.42