If you started today and borrowed S6000 every 6 MONTH until

If you started today and borrowed S6,000 every 6 MONTH until the end of 4 YEARS (8 borrow periods in total) in a student loan which carrys a nominal annual 3% interest rate compounded MONTHLY After 4 years, you start to pay back monthly over 10 year period. How much is your month payment? (period 0 $5,000, period 2 $5,000,., period $5,000) 7

Solution

As the compounding frequency and borrowing frequency are different, we can calculate each period’s interest and principal separately and then add to get the total borrowed amount along with interest.

Formula for compound interest is:

A = P x (1 +r) ⁿ

A = Principal + interest

P = Principal = $ 6,000 per period

r = rate of interest 3 % p.a. or 0.03/12 = 0.0025 monthly

n = No. of compounding periods = 48 for 1^st borrowing, 42 for 2^nd borrowing, 36 for 3^rd borrowing etc.

Period

Principal (P)

(1+r)ⁿ

Principal + interest (A)

1

$ 6,000

1.127328021

$ 6,763.97

2

$ 6,000

1.110565082

$ 6,663.39

3

$ 6,000

1.094051401

$ 6,564.31

4

$ 6,000

1.077783272

$ 6,466.70

5

$ 6,000

1.061757044

$ 6,370.54

6

$ 6,000

1.04596912

$ 6,275.81

7

$ 6,000

1.030415957

$ 6,182.50

8

$ 6,000

1.015094063

$ 6,090.56

                    Total

$ 51,377.78

Total borrowings along with interest is $ 51,377.78

Periodic repayment can be computed using formula for PV of annuity as:

PV = C x [1-(1+r)^-n/r]      

C = Periodic cash payment

r = Rate per period = 3 % or 0.03/12 = 0.0025 p.a.

n = Numbers of periods= 10 years x 12 months = 120

$ 51,377.78 = C x [1-(1+0.0025)^-120/0.0025]

          = C x [1-(1.025)^-120/0.0025]

          = C x [(1- 0.028809322)/0.0025]

          = C x (0.971190678/0.0025)

          = C x 32.37302261

C = 51,377.78 / 32.37302261

     = $ 1,587.06

Monthly loan repayment is $ 1,587.06

Period	Principal (P)	(1+r)n	Principal + interest (A)
1	$ 6,000	1.127328021	$ 6,763.97
2	$ 6,000	1.110565082	$ 6,663.39
3	$ 6,000	1.094051401	$ 6,564.31
4	$ 6,000	1.077783272	$ 6,466.70
5	$ 6,000	1.061757044	$ 6,370.54
6	$ 6,000	1.04596912	$ 6,275.81
7	$ 6,000	1.030415957	$ 6,182.50
8	$ 6,000	1.015094063	$ 6,090.56
		Total	$ 51,377.78