Question 252856: 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.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! It's a little unclear what you are asking.
Mixing annual compounding with monthly payments is not normally done.
You either get annual compounding with annual payments or monthly compounding with monthly payments.
The most commonly used interpretations for car loans or mortages is monthly compounding with monthly payments.
I'll use that interpretation below.
You are making monthly payments with monthly compounding on a loan that you took out today for $29,000 and need to pay off in 42 months.
The financial calculator inputs would be:
Present Value of the loan = $29,000
Number of Time periods is specified in months = 42.
Interest Rate per Time period is specified per month = .12 / 12 = .01
The financial calculator output would be:
Payment per Month = $848.99
42 months times $848.99 payments per month = $36,657.71
Interest you paid on the loan is equal to $36,657.71 - $29,000 = $6,657.71
If you need the formula, it is shown below:
PAYMENT FOR A PRESENT VALUE
PMT = Payment per Time Period
PV = Present Value
i = Interest Rate per Time Period
n = Number of Time Periods
The loan is equal to PV.
The numbmer of Time periods is 42 months.
The interest rate per time period is .12 / 12 = .01
You also mentioned sinking fund which leads me to believe you are looking for something entirely else.
If I want to have $29,000 in the future (at the end of 42 months, for example), then I would invest money in an account earing a certain percent interest and I would pay into that fund at specific time intervals.
Again, you would not normally mix annual compounding with annual payments.
Usually it's monthly payments with monthly compounding.
Assuming you want to make monthly payments into an account that is earning you 12% annually, and you want to have $29,000 at the end of the 42 months, then the financial calculator inputs and outputs would be as follows:
Inputs:
FV = Future Value = $29,000
i = interest rate per month = .12 / 12 = .01
n = Number of Time periods = 42 months.
Output:
Payment per month = $558.99
You would have payed into the account a total of 42 * $558.99 = $23,477l.71
You would have withdrawn $29,000 at the end of the 42 months.
The interest you earned would be equal to $29,000 minus $23,4771.71 = $5,522.29
If you need the formula for this scenario, it is shown below:
PAYMENT FOR A FUTURE VALUE
PMT = Payment per Time Period
FV = Future Value
i = Interest Rate per Time Period
n = Number of Time Periods
FV = $29,000 which is the amount of money you want to have at the end of the investment period.
i = interest rate per month = .12 / 12 = .01
n = number of months = 42
|
|
|
