SOLUTION: Mark and Kate are establishing a fund for their son's college education. What lump sum must they deposit in an account that gives 8% annual interest rate, compounded monthly, in or

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Question 153154: Mark and Kate are establishing a fund for their son's college education. What lump sum must they deposit in an account that gives 8% annual interest rate, compounded monthly, in order for them to have $60,000 in the account at the end of 10 years?
Can anyone help me out? Please and thank you!
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
If the bank offers monthly compounding, then at the end of n months the total amount, T, in their bank will be:
T+=+P%281+%2B+r%29%5En
where P is the principal, r is the monthly interest rate.
Substituting
T = 60,000
n = 10*12 = 120
r = 8%/12 = 1/3%= 0.0033333
into the formula, we have
60000+=+P%281%2B0.003333%29%5E120
Solving for P, we have
P+=+60000%2F%281.003333%29%5E120
ln+P+=+ln+%2860000%29-120%2Aln+%281.003333%29
ln+P+=+11.0021-120%2A0.003327
ln+P+=+10.6029
So
P = 40251