Find the future value!
Periodic payment: $650.00
Payment interval: every month
Term: 19 years, 2 months
Interest rate: 4.75%
Compound frequency: monthly
To find the future value of the periodic payments, we can use the formula for the future value of an annuity:
Future Value = Payment × (((1 + Interest Rate / Compound Frequency)^(Compound Frequency × Term)) - 1) / (Interest Rate / Compound Frequency)
Let's plug in the values provided:
Payment = $650.00
Interest Rate = 4.75% (expressed as a decimal, so 4.75 / 100 = 0.0475)
Compound Frequency = monthly = 12
Term = 19 years, 2 months = 19 years + 2/12 years = 19.16667 years
Future Value = $650.00 × (((1 + 0.0475 / 12)^(12 × 19.16667)) - 1) / (0.0475 / 12)
Now let's calculate it step by step:
Step 1: Calculate the inside parentheses first.
(1 + 0.0475 / 12) = 1.003958333 (rounded to 9 decimal places)
Step 2: Calculate the exponent.
(12 × 19.16667) = 229.99964 (rounded to 5 decimal places)
Step 3: Raise the number from Step 1 to the power of the number from Step 2.
(1.003958333)^229.99964 = 3.797620149 (rounded to 9 decimal places)
Step 4: Calculate the final part of the formula.
(3.797620149 - 1) / (0.0475 / 12) = 89.01669999 (rounded to 8 decimal places)
Step 5: Multiply the payment by the result from Step 4.
$650.00 × 89.01669999 = $57,761.05 (rounded to 2 decimal places)
Therefore, the future value of the periodic payments is $57,761.05.