Grandparents of a new-born child want to invest money in a college fund so that their grandchild will have $50,000 at the age 18. The interest rate at the bank

Question

Grandparents of a new-born child want to invest money in a college fund so that their grandchild will have $50,000 at the age 18. The interest rate at the bank is 4.25%. If the maximum amount that the grandparents have to invest is $5,000, what interest rate(continuously compounded interest) would they need to have $50,000 in 18 years?

Answer 1

The formula for continuous compounding is Continuous Compounding is

FV = PV*e^rt where e is the constant whose approximate value is 2.71858, r is the interest rate and t is time.

 

FV = 5,000*e^(.0425*18) = 10,744.97

 

To have 50,000 after 18 years

50,000 = 5,000 * e^(r*18) and you have to solve for r.

 

The interest rate would have to be abut 12.8 percent. A financial calculator solves this easily. It is worthwhile having one, but you still have to understand compound interest concepts.