Solve This Problem

Question

When Jason Levy was born, his grandparents deposited $3,000 into a special account for Jason's college education. The account earned 6 1/2% interest compounded daily. How much will be in the account when Jason is 18? (Give your answer to the nearest cent.)

Answer 1

A=P(1+r/n)^nt

with P=3000 dollars

r=6.5%=.065

t= 18 years

n= number of compounding periods per year = 365.25

plug the numbers in

3000(1+.065/365.25)^365.25(18)== $9,664.97 rounded to nearest cent

= Amount in 18 years with $3,000 compounded daily at 6.5% interest

use a calculator

. for more precise answer use 3.65.25 in place of 365 for leap years

in 18 years there should be about 18/4 = 4 1/2 leap years on average

365 1/4 days per year

check the answer as daily compounding is very close to continual compounding

A=Pe^rt

3000e^.065(18) = 9665.98 Close enough. just a dollar and a penny difference. Continual compounding should be slightly more than daily compounding