Algebra II

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 of 18. The interest rate at ultimate bank is 4.25%.
a). If the interest was compounded continuously, how much money will they have to invest?
b). 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

Set 50000 equal to P(1 + 0.0425 ÷ n)^[18×n].

For a large value of n (such as n=10⁸), P(1 + 0.0425 ÷ n)^[18×n] has

been proven by Calculus equal to Pe^{{0.0425 × 18}}

where e [the base of the natural logarithm] is equal

to 2.7182818284590452353602874713527.

Then 50000 divided by e^{{0.0425 × 18}} gives the

principal P required as $23266.69655 equivalent

to $23266.70.

Next, 50000 = 5000 × e^{{R × 18}} translates to 10 = [e^{18}]^R or

ln 10 = R × ln [e^{18}] which isolates the interest rate R sought

as 0.1279213941 (roughly 12.79 percent).