Answer:
A.50 months
B.12.92 months
C.$112.38
Explanation:
a). Using this formula
PV of Annuity = Monthly Payment * [{1 - (1 + r)-n} / r]
Where,
PV of Annuity =$350
Monthly Payment =$10
r=(0.18/12)
Let plug in the formula
$350 = $10 * [{1 - (1 + 0.18/12)-n} / (0.18/12)]
$350 / $10 = {1 - (1.015)-n} / 0.015
35 * 0.015 = 1 - (1.015)-n
(1.015)-n = 1 - 0.525
-n[log(1.015)] = log(0.475)
-n[0.0149] = -0.7444
n = -0.7444 / -0.0149
n= 50 months
b). Using this formula
PV of Annuity = Monthly Payment * [{1 - (1 + r)-n} / r]
Where,
PV of Annuity =$350
Monthly Payment =$30
r=(0.18/12)
Let plug in the formula
$350 = $30 * [{1 - (1 + 0.18/12)-n} / (0.18/12)]
$350 / $30 = {1 - (1.015)-n} / 0.015
11.67 * 0.015 = 1 - (1.015)-n
(1.015)-n = 1 - 0.175
-n[log(1.015)] = log(0.825)
-n[0.0149] = -0.1924
n = -0.1924 / -0.0149 =
n=12.92 months
c). Calculation for the Total Amount Paid under $10-a-month plan
Using this formula
Total Amount Paid under $10-a-month plan = No. of Payments * Monthly Payment
Where,
No.of Payments =50
Monthly Payment=10
Let plug in the formula
Total Amount Paid under $10-a-month plan= 50 * $10 = $500
Calculation for the Total Amount Paid under $30-a-month plan
Using this formula
Total Amount Paid under $30-a-month plan = No. of Payments * Monthly Payment
Where,
No. of Payments =12.92
Monthly Payment=$30
Let plug in the formula
Total Amount Paid under $30-a-month plan= 12.92 * $30 = $387.62
Hence,
Total Amount Paid under $10-a-month plan -Total Amount Paid under $30-a-month plan
= $500 - $387.62
= $112.38
