PROBLEM SOLVING : CERTIFIED FINANCIAL PLANNER
If an individual put the equivalent of $50 per month, or $600 annually into an ordinary annuity, how much money would accumulate in 20 years at 3% compounded annually? How much at 5%?
To find out how much money would accumulate in 20 years at different interest rates, we can use the formula for the future value of an ordinary annuity:
Future Value = P * ((1 + r)^n - 1) / r
Where:
- P is the periodic payment (monthly or annually in this case)
- r is the interest rate per compounding period
- n is the number of compounding periods (in this case, 20 years)
Let's calculate the future value at a 3% interest rate:
P = $50 per month = $50 * 12 = $600 annually
r = 3% = 0.03
n = 20 years
Future Value = $600 * ((1 + 0.03)^20 - 1) / 0.03
= $600 * (1.03^20 - 1) / 0.03
To calculate this, you can use a financial calculator, spreadsheet software, or online financial calculators. The future value at 3% interest would be approximately $15,100.
Now let's calculate the future value at a 5% interest rate:
P = $600 annually
r = 5% = 0.05
n = 20 years
Future Value = $600 * ((1 + 0.05)^20 - 1) / 0.05
= $600 * (1.05^20 - 1) / 0.05
Again, you can use a financial calculator, spreadsheet software, or online financial calculators. The future value at 5% interest would be approximately $21,500.