Determine the amount of each payment to be made to a sinking fund in order that enough money will be available to pay off the following loan.
$29,000 loan, money earns 12% compounded annually, 42 months.
I tired doing this using the future value of an ordinary annuity formula, but get a number below zero...not sure what I am doing wrong.
To determine the amount of each payment to be made to a sinking fund, you can use the formula for the future value of an ordinary annuity:
A = P * (1 + r)^n - 1 / r
Where:
A = future value of the annuity
P = payment amount
r = interest rate per compounding period
n = number of compounding periods
In this case, you need to calculate the future value (A) of the annuity to determine how much money is needed to pay off the loan.
Given:
Loan amount (P) = $29,000
Interest rate (r) = 12% per year (or 0.12)
Number of compounding periods (n) = 42 months
First, convert the interest rate to the rate per compounding period. Since it is compounded annually, divide the annual interest rate by 12 (the number of months in a year):
r = 12% / 12 = 0.01
Next, convert the number of months to the number of compounding periods. Since the interest is compounded annually, divide the number of months by 12:
n = 42 months / 12 = 3.5 years
Now, substitute the values into the formula:
A = $29,000 * (1 + 0.01)^3.5 - 1 / 0.01
After simplifying the equation, you should get the future value (A). This represents the total amount of money needed to pay off the loan.
If you obtained a negative value, double-check your calculations and ensure you have used the correct formula.