Question

17. You invest $4000 in an account to save for college.

a. Option 1 pays 5% annual interest compounded semi-annually. What would
be the balance in the account after 2 years?
b. Option 2 pays 4.5% annual interest compounded continuously. What would
be the balance in the account after 2 years?
c. At what time t (in years) would Option 1 give you $100 more than Option 2?

Answer 1

a. $4,415.25

b. $4,376.70

c. 2.27986 years

Explanation:

a.

A = 4,000 (1 + 0.05/2)^(2 x 2)

= $4,415.25

b.

A = 4,000 x e^(0.045 x 2)

= $4,376.70

c. $100 more than option 2 = 4,376.70 + 100

= $4,476.70

t (in years) = ln(4,476.70/4,000) / ln(1 + 0.05/2)

= 2.27986 years