Precalculus Question

Question

Heather wants to invest $35,000 of her retirement. She can invest at 4.8% simple interest for 20 yr, or she can choose an option with 3.6% interest compounded continuously for 20 yr. Which option results in more total interest?

Answer 1

GIVEN:

Principal, P = $35,000; time, t = 20 years

simple interest rate, r_s = 4.8% = 0.048, continuous interest rate r = 3.6% = 0.036

Simple Interest Formula:

Interest = I = (Principal) * (Rate) * (Time) = P*r_s*t

so,

I = 35000 * 0.048 * 20 = $33,600

Continuous Compounded Interest Formula:

Future Amount = A = P * e^rt

and,

Interest = I = A - P

so,

A = 35000 * e ^{0.036 * 20} = $71,905.16;

I = 71,905.16 - 35,000 = $36,905.16, which is the greater interest amount of the two methods.

Answer 2

A)

A = 35000(1 + 0.048)(20)

B)

A = 35000e^(0.048)(20)