If a father wants to have $100,000 to send a newborn child to college, how much must he invest annually for 18 years if he earns 9 percent on his funds?
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To find out how much the father must invest annually for 18 years to accumulate $100,000, we can use the concept of compound interest.
Compound interest calculation formula:
Future Value (FV) = Present Value (PV) * (1 + interest rate)^n
Where:
FV = Future Value (desired amount, which is $100,000 in this case)
PV = Present Value (amount to be invested annually)
Interest rate = Annual interest rate (9 percent)
n = Number of years (18 years)
Let's plug in the values into the formula and solve for PV (the amount to be invested annually):
$100,000 = PV * (1 + 0.09)^18
Now, let's solve for PV:
PV = $100,000 / (1 + 0.09)^18
Calculating this value will give us the annual investment needed.
Using a calculator or spreadsheet, the calculation is as follows:
PV = $100,000 / (1.09)^18
≈ $100,000 / 3.172382
≈ $31,573.28
Therefore, the father needs to invest approximately $31,573.28 annually for 18 years at a 9 percent interest rate to accumulate $100,000 for sending the newborn child to college.