To do this we use the formula for the present value of an ordinary annuity and solve it for PMT. i Solving for PMT yields PMT = PV- 1-(1+i)-n To use the above formula, first calculate i and n. rate written as a decimal i= # of periods per year n = (# of years) • (# of periods per year) %3D Present 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 Note: Payments are made at the end of each period.

Question

A sailboat costs $30,215. You pay 25% down and amortize the rest with equal monthly payments over a 15​-year period. If you must pay 6.6% compounded​ monthly, what is your monthly​ payment? How much interest will you​ pay?

a) To solve the​ problem, we will need to calculate the monthly payment on the​ sailboat's cost minus the down payment. (attached picture to help problem - called Equations to help problem A)

Monthly​ payments: $____ (round to two decimal​ places)

 

b) Total interest paid equals =​ (amount of all ​payments) - ​(initial loan)

The total interest paid on the loan is $_____

 

To do this we use the formula for the present value of an ordinary annuity and solve it for PMT.
i
Solving for PMT yields PMT = PV-
1-(1+i)-n
To use the above formula, first calculate i and n.
rate written as a decimal
i=
# of periods per year
n = (# of years) • (# of periods per year)
%3D
View transcribed image text
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Present 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
Note: Payments are made at the end of each period.
View transcribed image text
Expand

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Transcribed Image Text

To do this we use the formula for the present value of an ordinary annuity and solve it for PMT. i Solving for PMT yields PMT = PV- 1-(1+i)-n To use the above formula, first calculate i and n. rate written as a decimal i= # of periods per year n = (# of years) • (# of periods per year) %3D

Present 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 Note: Payments are made at the end of each period.