Question

Sabrina purchased a dining room set for $2,390 using a 12-month deferred payment plan with an interest rate of 24.28%. She did not make any payments during the deferment period. What will Sabrina’s monthly payment be if she must pay off the dining room set within two years after the deferment period?

$161.12

$126.64

$99.58

$136.55

Answer 1

i actually think i know this but im spacing out so hard right now.. ADD<3

Answer 2

Since no payments were made during the deferment period, back interest will be calculated at the end of the 12-month deferment period and added on to the old principal which will be the new principal that needs to be paid off in 2 years.

First use the compound interest formula to calculate the principal + interest during the deferment period: \[\Large A = P(1 + \frac{ r }{ n })^{nt}\]where:
A = Amount at maturity or the amount due at the end of the deferment period
P = Principal Amount
r = Annual interest rate in decimal
n = compounding period (compounded how many times a year) (=12 here, since compounded monthly))
t = years invested (here t = 1 year)

The A calculated above will be the amount due or the loan amount to be repaid in full in 2 years or 24 months. Use the monthly payment formula that is used in mortgage calculations:\[\Large M = \frac{Lc(1+c)^n} {(1+c)^n - 1}\]where:
M = Fixed Monthly Payment
L = Total Loan Amount (=A from the previous calculation)
c = Interest rate in decimal PER MONTH where the interest rate is assumed to be compounded monthly
n = Total number of monthly payments

Plug in the numbers and calculate M.