Jason and Mary have a new baby. They want to invest $20,000 at the baby’s birth in order to have $100,000 for the baby’s college education. What interest rate do they need to earn in order to achieve this in 18 years?

Question

Use the following formula to determine the average interest rate:
r = (S/P)^1/n – 1

where S = the final amount
P = the initial investment
n = number of years

Answer 1

yes. S = P (1+r)^n

100 = 20 (1+r)^18
(1+r)^18 = 5
18 log (1+r) = log 5
using base 10 logs
18 log(1+r) = .699
log(1+r) = .0388
take antilog
1+r = 1.0935
r = .0935
times 100 = 9.35 %

Answer 2

Thanks for the help but I still don't understand. What does log and antilog stand for?