Jenny and Dan want to save for an RV.They estimate that they will need $15,000 in 8 years. They can get 3% interest compounded semiannually. How much would they need to deposit now in order to have $15,000 in 8 years ? Put answer to the nearest cent.
2 answers
15000 = x [1 + (.03 / 2)]^(8 * 2)
Standard compound interest formula:
F=P(1+i/k)^(kn)
F=future value (in eight years)
P=present value (amount of deposit)
i=APR=nominal annual interest rate (0.03)
k=number of compounding per year (2)
n=number of years
=>
P=F/(1+i/k)^(kn)
=15000/(1+.03/2)^(2*8)
=15000/(1.015^16)
=11820.466
(check my numbers)
F=P(1+i/k)^(kn)
F=future value (in eight years)
P=present value (amount of deposit)
i=APR=nominal annual interest rate (0.03)
k=number of compounding per year (2)
n=number of years
=>
P=F/(1+i/k)^(kn)
=15000/(1+.03/2)^(2*8)
=15000/(1.015^16)
=11820.466
(check my numbers)