Question

5. What is the monthly interest rate you are paying to Jane the Loan Shark if you borrow $1,000 today and pay back $100 each month for 11 months and then $700 a year from today?

Answer 1

Inorder to find out the interest %, we shall equate present value of payment to loan taken. we will use trial and error method. The rate at which NPV becomes zero will be the interest rate.

First we are taking 5% monthy discount rate.

MONTHS	CASHFLOW	DISCOUNT FACTOR @ 5% PER MONTH	PRESENT VALUE
0	-$1,000	1.0000	-$1,000.00
1	$100	0.9524	$95.24
2	$100	0.9070	$90.70
3	$100	0.8638	$86.38
4	$100	0.8227	$82.27
5	$100	0.7835	$78.35
6	$100	0.7462	$74.62
7	$100	0.7107	$71.07
8	$100	0.6768	$67.68
9	$100	0.6446	$64.46
10	$100	0.6139	$61.39
11	$100	0.5847	$58.47
12	$700	0.5568	$389.79
		NPV =	$220.43

Since we have positive NPV, we will try a discount rate higher.

Let us take monthly discount rate as 7%

MONTHS	CASHFLOW	DISCOUNT FACTOR @ 7% PER MONTH	PRESENT VALUE
0	-$1,000	1.0000	-$1,000.00
1	$100	0.9346	$93.46
2	$100	0.8734	$87.34
3	$100	0.8163	$81.63
4	$100	0.7629	$76.29
5	$100	0.7130	$71.30
6	$100	0.6663	$66.63
7	$100	0.6227	$62.27
8	$100	0.5820	$58.20
9	$100	0.5439	$54.39
10	$100	0.5083	$50.83
11	$100	0.4751	$47.51
12	$700	0.4440	$310.81
		NPV =	$60.68

Since we have positive NPV, we will try higher discount rate.

Let us take monthly discount rate as 8%

MONTHS	CASHFLOW	DISCOUNT FACTOR @ 8% PER MONTH	PRESENT VALUE
0	-$1,000	1.0000	-$1,000.00
1	$100	0.9259	$92.59
2	$100	0.8573	$85.73
3	$100	0.7938	$79.38
4	$100	0.7350	$73.50
5	$100	0.6806	$68.06
6	$100	0.6302	$63.02
7	$100	0.5835	$58.35
8	$100	0.5403	$54.03
9	$100	0.5002	$50.02
10	$100	0.4632	$46.32
11	$100	0.4289	$42.89
12	$700	0.3971	$277.98
		NPV =	-$8.12

Since we have a negative NPV, Rate at which NPV = 0 will be between 7% and 8%.

Therefore IRR = 7% + [$60.68 / ($60.68 + $8.12)]

= 7.88% per month

So interest rate paid is 7.88% per month