Business

FinanceQ&A LibraryPresent Value of an Ordinary Annuity 1- (1 + i) PV = PMT- i where PV = present value of all payments PMT = periodic payment i= rate per period (written as a decimal) n= number of periods %3D Note: Payments are made at the end of each period. a. To find the monthly payment, use the formula for the present value of an ordinary annuity and solve it for PMT. Now find the total interest paid. Total interest paid = (amount of all payments) - (initial loan) Present Value of an Ordinary Annuity -n 1-(1 + i) PV = PMT- where PV = present value of all payments PMT = periodic payment i= rate per period (written as a decimal) n= number of periods %3D %3D Note: Payments are made at the end of each period. b. To find out how long it will take to pay off the mortgage by paying an extra $100 a month requires the use of a new formula that has n, the number of periods, as the dependent variable. We want to start with the formula for the present value of an ordinary annuity and then use logarithms to solve it for n. 1-(1+ i) -n PV = PMT: Original equaton. i• PV log 1 1-(1+ i)" PMT Therefore, solving PV = PMT for n yields n= log(1 + i) Of the three variables on the right side of the new equation for n, the PV amd i will stay the PMT will change. Now find the total interest paid. Total interest paid = (amount of all payments) – (initial loan)Question

A family has a $145,247, 15-years mortgage at 5.7 % compounded monthly.

Monthly payment: $____ *(Round to two decimal places.)*

Total interest paid: $____ *(Round to two decimal places.)*

Time: ____ years *(Round to two decimal places.)*

Total interest paid: $____ *(Round to two decimal places.)*

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