Question

1. Consider the following situation where the borrowing of P is repaid in two payments in the years 3 and 5: Year Cash flow 0 +P 1 20 3 -400 40 5S -600 Construct a cash flow diagram. Solve for P assuming a 12% interest rate and using the compound interest tables.

Answer 1

Solution,

Here P doller has been received time zero. $400 is paid after 2 years ad $600 after 5 years. So cash flow diagram is-

In this problem P doller has been borrowed at time 0. Interest is payable at 12%. Payment has been made in two instalments. First one is paid after 3 years. Amount is 400. It included interest for 3 years on p doller. Balance amount along with interest for 2 tearsnis repaid. Thus-

1. Loan taken on time 0	P
2. Add: Interest at 12% for 3 years [PX(1.12)3 -P]	0.404928P
3. Total amount due at the end of year 3 [1+2]	1.404928P
4. Less: amount paid after 3 years	400
5. Balance left at the start of 4th year [3-4]	1.404928P-400
6. Add: Interest for 4th year [1.404928P-400]*0.12	0.16859136P-48
7. Total dues at the end of 4th year [5+6]	1.5735193P-448
8. add: Interest of 5th year [1.5735193P-448]*0.12	0.1888223P-53.76
9. Total dues at the end of 5th year [7+8]	1.7623416P-501.76
10. Paid at the end of 5th year	600
11. Balance due [9-10]	0

Therefore,

1.7623416P - 501.76 = 600

1.7623416P = 1101.76

1.7623416P = 625.168

Thus loan taken is $625 (rounded off to nearest doller).