Question

You need to take a loan of $1,500. You have two repayment options:

Option 1: Short-term 6% interest loan with a term of 1 year.

Option 2: 1-year simple interest amortized loan at 6% interest, monthly payments.

1.) Calculate the lump sum payment for plan A. Then calculate the monthly payment for plan B. Explain how you arrived at your answer. You do not need to copy the formulas here; simply explain what formulas you used and how you used them.

2.) Calculate the total interest paid for both plans. Explain why you pay more interest with one of the options, and which option you would prefer

Answer 1

1) Option 1: Simple Interest on the loan @ 6%

Interest = Principal*Rate of interest * No.of years

= $ 1500*6%*1

= $ 90

Total amount to be repaid = Principal + Interest

= $ 1500+$ 90

= $ 1590

Hence lumpsum paymemt is $ 1590.

Option 2: Interest rate per Year = 6 % p.a

Interest rate per month = 6% /12 = 0.5% per month

We know that the Present value of the future cash outflows is equal to the loan amount

Let the Monthly installment be X

X * PVAF( 0.5%,12) = $ 1500

X * 11.61893 = $ 1500

X = $ 1500/11.61893

X = 129.0996

Hence Monthly payyment is $ 129.0996

2) Interest under option 1 or Plan A = $ 90

Interst under option B:

Total amount paid = $ 129.0996*12 = $ 1549.1952

less : Principal amount = $ 1500

Interest = $ 49.1952

Interest under option B is $ 49.20

I would prefer option 2 or plan B

We can observe that more interest is paid when there is a lumpsum amount . This is because no priincipal is repaid during the year.So interest falls on Entire amount.Whereas in option B , Every year someportion of the principal get repaid along with the interest. So for every payment principal portion goes on increaseing and interest portion is decreasing

Month	Opening Balance	Interest @ 0.5%	Total	Amount paid	Principal portion	Closing Balance
1	$1,500	$7.50	$1,507.50	$129.0996	$121.5996	$1,378.40
2	$1,378.40	$6.89	$1,385.29	$129.0996	$122.2076	$1,256.19
3	$1,256.19	$6.28	$1,262.47	$129.0996	$122.8186	$1,133.37
4	$1,133.37	$5.67	$1,139.04	$129.0996	$123.4327	$1,009.94
5	$1,009.94	$5.05	$1,014.99	$129.0996	$124.0499	$885.89
6	$885.89	$4.43	$890.32	$129.0996	$124.6701	$761.22
7	$761.22	$3.81	$765.03	$129.0996	$125.2935	$635.93
8	$635.93	$3.18	$639.11	$129.0996	$125.9200	$510.01
9	$510.01	$2.55	$512.56	$129.0996	$126.5496	$383.46
10	$383.46	$1.92	$385.38	$129.0996	$127.1823	$256.28
11	$256.28	$1.28	$257.56	$129.0996	$127.8182	$128.46
12	$128.46	$0.64	$129.10	$129.0996	$128.4573	$0.00

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