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.
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)
To find out how much Jenny and Dan would need to deposit now in order to have $15,000 in 8 years, we can use the formula for compound interest.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A is the final amount (in this case, $15,000)
P is the principal amount (the initial deposit we want to find)
r is the annual interest rate (3% in this case)
n is the number of times that interest is compounded per year (semiannually, so 2)
t is the number of years (8 in this case)
We need to rearrange this formula to solve for P:
P = A / (1 + r/n)^(nt)
Now let's plug in the values:
A = $15,000
r = 0.03 (3% as a decimal)
n = 2 (semiannual compounding)
t = 8 years
P = 15000 / (1 + 0.03/2)^(2*8)
Now we can calculate the result:
P = 15000 / (1 + 0.015)^(16)
P = 15000 / (1.015)^16
P = 15000 / 1.270678
P ≈ $11,799.39
Therefore, Jenny and Dan would need to deposit approximately $11,799.39 now in order to have $15,000 in 8 years.