Question

Using technology, determine the present value given that you make monthly payments of $250.00 at 2.3% compounded monthly over a 5 year period. Round your answer to the nearest cent.

a.
$10,776.33
b.
$8,046.04
c.
$14,156.84
d.
$14,165.26

Answer 1

The correct option is c.

Explanation:

Given information: monthly payments = $250.00, Interest rate = 2.3% compounded monthly over a 5 year period.

The formula for monthly payment:

`C=(PV((r)/(n)))/(1-(1+(r)/(n))^(-n*t))`

Where, C is monthly payment, r is rate of interest, n is number of times interest compounded in a year, t is number of years, PV is present value.

`250=(PV((0.023)/(12)))/(1-(1+(0.023)/(12))^(-12*5))`

`250=(PV((0.023)/(12)))/(1-(1+(0.023)/(12))^(-60))`

`250(1-(1+(0.023)/(12))^(-60))=PV((0.023)/(12))`

`(250(1-(1+(0.023)/(12))^(-60)))/(((0.023)/(12)))=PV`

`14156.83566=PV`

`14156.84\approx PV`

The present value is 14156.84.

Therefore the correct option is c.