Answer:
Always the second option will be better because 31 payments x $900 = $27,900, no matter what interest rate you use, it cannot be negative.
Explanation:
A) two options:
$32,500 now or $900 in 31 months
to determine by how much the installment plan is is better, we need to determine the present value of the annuity:
present value = payment x {[1 - 1/(1 + r)ⁿ] / r}
- r = 7% / 12 = 0.58333%
- payment = $900
- n = 31
present value = $900 x {[1 - 1/(1 + 0.0058333)³¹] / 0.0058333} = $25,455
with this plan you save = $32,500 - $25,455 = $7,045
B) if the interest rate is higher, you save even more money:
present value = payment x {[1 - 1/(1 + r)ⁿ] / r}
- r = 19% / 12 = 1.58333%
- payment = $900
- n = 31
present value = $900 x {[1 - 1/(1 + 0.0158333)³¹] / 0.0158333} = $21,914
with this plan you save = $32,500 - $21,914 = $10,586
