Question

A company purchased equipment and signed a 7-year installment loan at 9% annual interest. The annual payments equal $9,000. The present value of an annuity factor for 7 years at 9% is 5.0330. The present value of a single sum factor for 7 years at 9% is 0.5470. The present value of the loan is:

A. $9,000
B. $4,923
C. $16,453
D. $63,000
E. $45,297

Answer 1

Here we apply the present value of annuity formula. This formula is given by:
P=A[(1-1/()1+r)^n]/r
where:
P=present value
A=future value
r=rate
n=number of terms
NOTE:
[(1-1/()1+r)^n]/r
is called the present value of annuity factor, this has been given as 0.5033.
Thus our formula can be written as:
P=5.033A
Thus to evaluate the present value we plug in the values in our formula:
hence:
P=5.033(9000)
P=45297

Answer 2

First, we should apply the present value of annuity formula. It is
`PV=A (1- (1)/((1+r)^(N)))/(r)` and in this formula
`(1- (1)/((1+r)^(N)))/(r)` is the present value of annuity factor.

Then, we can find the present value of the annuity by writing that,
`PV=9000 * 5.033 = 45297`