Question

John bought a new computer for $1,650. He paid a $160 down payment and financed the rest for 1 year at an interest rate of 7%. Find the total interest paid on the given amortized loan assuming that John makes monthly payments.

Answer 1

choices are a)52.66 b)63.84 c)67.76 d)57.10

Answer 2

Basic Principles ALWAYS solves the problem - always.

i = 0.07 -- Annual Interest Rate
j = 0.07/12 = 0.0058333... -- Monthly Interest Rate
r = 1+j = 1.0058333... -- Monthly Accumulation Factor
v = 1/r = 0.99420 -- Monthly Discount Factor

We have 12 payments, one month apart, and starting one month after purchase.

1650 - 160 = Pmt(v + v^2 + v^3 + ... + v^12)

Do you know how to add up those 'v's?

Answer 3

I don't know how to add the v's

Answer 4

You've probably seen it. Free demonstration of adding up finite geometric series:

Call the sum something.
1) v + v^2 + v^3 + ... + v^12 = S

2) Multiply by the common ratio
v^2 + v^3 + ... + v^12 + v^13 = Sv

Subtract 2) from 1)

v - v^13 = S - Sv

Solve for S: \(S = \dfrac{v - v^{13}}{1-v}\)

More simplifications will make it look more familiar, but this is it!

1650 - 160 = Pmt(v - v^13)/(1-v)

Solve for Pmt.