Answer to Question #139328 in Financial Math for Warisha

Question

A loan of £100000 is repayable by equal quarterly payments for 4 years. The effective rate of interest is 7% pa.
Required:
1. Find the equal quarterly payment amount
2. Draw the amortisation schedule for the loan repayment
3. What is the interest portion paid on the 6th payment?
4. What is the total interest paid after the 12th payment?

Answer 1

1. find the total amount of payment for the loan:

$P=\frac{L}{\frac{(1 + r) ^ n - 1)}{(r * (1 + r) ^ n)}}=\frac{100 000}{\frac{(1 + 0.0175) ^ {16} - 1)}{(0.0175 * (1 + 0.0175) ^ {16})}}=7219.96$

2.the amortization schedule for the loan repayment: 

P i

0 0 0 100 000.00

1 7 219.96 1 750.00 5 469.96 94 530.04

2 7 219.96 1 654.28 5 565.68 88 964.36

3 7 219.96 1 556.88 5 663.08 83 301.28

4 7 219.96 1 457.77 5 762.19 77 539.09

5 7 219.96 1 356.93 5 863.03 71 676.06

6 7 219.96 1 254.33 5 965.63 65 710.43

7 7 219.96 1 149.93 6 070.03 59 640.40

8 7 219.96 1 043.71 6 176.25 53 464.15

9 7 219.96 935.62 6 284.34 47 179.81

10 7 219.96 825.65 6 394.31 40 785.50

11 7 219.96 713.75 6 506.21 34 279.29

12 7 219.96 599.89 6 620.07 27 659.22

13 7 219.96 484.04 6 735.92 20 923.30

14 7 219.96 366.16 6 853.80 14 069.50

15 7 219.96 246.22 6 973.74 7 095.76

16 7 219.94 124.18 7 095.76 0

115 519.34 15 519.34 100 000.00 0

since the loan is repaid in equal parts, each payment is 7219.96, which consists of the amount of debt and interest, and the loan amount is reduced by this payment amount each time

interest on the loan can be found using the following formula:

$г1=100 000(\frac{0.07}{4})=1750$

7219.96-1750=5469.96 - amount of debt in payment

in this way, we calculate each time the remaining debt, interest, and debt in payment for all payment periods

3.The share is calculated using the ratio of the amount or product of the first 6 payments to the total amount of payments on the loan according to the amortization schedule for the loan repayment:

$\frac{7219.96*6}{115519.34}\times100=37.50$ %

4.the total amount of interest on 12 payments is calculated by the amount of interest on 12 payments according to the amortization schedule for the loan repayment:

$\sum_{i1+i2+i3+i4+i5+i6+i7+i8+i9+i10+i11+i12}=14298.74$

or you can read it using the above formula:

each time we subtract the amount of debt in the payment from the balance of the loan and multiply it by the interest rate and add everything up$100 000(\frac{0.07}{4})+(100 000-5469.96)(\frac{0.07}{4})+....+(100 000-5469.96-5565.68-5663.08-5762.19-5863.03-5965.63-6070.03-6176.25-6284.34-6394.34-6506.31-6620.07))(\frac{0.07}{4})=14298.74$