Question

Shirley, a recent college​ graduate, excitedly described to her older sister the ​$1,670 ​sofa, table, and chairs she found today.​ However, when asked she could not tell her sister which interest calculation method was to be used on her​ credit-based purchase. Calculate the monthly payments and total cost for a bank loan assuming a​ one-year repayment period and 14.5 percent interest. Now assume the store uses the​ add-on method of interest calculation. Calculate the monthly payment and total cost with a​ one-year repayment period and 12.5 percent interest. Explain why the bank payment and total cost are lower even though the stated interest rate is higher. The monthly payment for a bank loan assuming​ one-year repayment period and 14.5 percent interest is ​$? The total cost for a bank loan assuming​ one-year repayment period and 14.5 percent interest is ​$? If the store uses the​ add-on method of interest​ calculation, the monthly payment with a​ one-year repayment period and 12.5 percent interest is ​$? If the store uses the​ add-on method of interest​ calculation, the total cost with a​ one-year repayment period and 12.5 percent interest is $?

Answer 1

PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream	1670
PMT = the dollar amount of each annuity payment	to be calculated
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate	14.5%/12	1.21%
n = the number of periods in which payments will be made	12
1670=	PMT *(((1-(1 + 1.21%) ^- 12)) / 1.21%)
1670=	PMT * 11.1083
Per month payment	1670/11.1083
Per month payment	150.34
Total payment done	1,804.06
Cost	1,670.00
Total finance cost	134.06
Add on method
Loan	1,670.00
Interest	12.50%
Total Interest	=1670*0.125
	208.75
Total payable	=1670+208.75
	1,878.75
EMI	1878.75/12
EMI	156.56
Since the annuity method considers the time value of money on principal being paid every month, the bank payment and total finance cost if lower even with the high-interest rate