__AFB Last Minute Revision__

Paper III

Paper III

We have,

Periodic Payment R = 5,000

Number of Periods n = 12

Interest Rate i = 12%/12 = 1%

Present Value

PV = 5000 × (1-(1+1%)^(-12))/1%

= 5000 × (1-1.01^-12)/1%

= 5000 × (1-0.88745)/1%

= 5000 × 0.11255/1%

= 5000 × 11.255

= 56,275.40

2. A certain amount was invested on Jan 1, 2015 such that it generated a periodic payment of 10,000 at the beginning of each month of the calendar year 2015. The interest rate on the investment was 13.2%. Calculate the original investment and the interest earned.

Periodic Payment R = 10,000

Number of Periods n = 12

Interest Rate i = 13.2%/12 = 1.1%

Original Investment= PV of annuity due on Jan 1, 2015

= 10,000 × (1-(1+1.1%)^(-12))/1.1% × (1+1.1%)

= 10,000 × (1-1.011^-12)/0.011 × 1.011

= 10,000 × (1-0.876973)/0.011 × 1.011

= 10,000 × 0.123027/0.011 × 1.011

= 10,000 × 11.184289 × 1.011

= 1,13,073.20

Interest Earned = 10,000 × 12 − 1,13,073.20

= 1,20,000 – 1,13,073.20

= 6926.80

3. A sum of Rs 12,500 amounts to Rs. 15,500 in the 4 years at the rate of simple interest. Find the rate percent? S.I.=P*R*T/100

=>R=S.I.*100/P/T

So, S.I = 15500 - 12500 = 3000.

=>R = 3000*100/12500/4

= 6%

4. A bond, whose par value is Rs. 1,000, bears a coupon rate of 12 per cent and has a maturity period of 3 years The required rate of return on the bond is 10 per cent. What is the value of this bond?

Annual interest payable = 1,000 * 12% = 120

Principal repayment at the end of 3 years = Rs. 1,000

The value of the bond

= 120 (PVIFA 10%, 3 yrs) + Rs. 1,000 (PVIF 10%, 3 yrs)

= 120 (2.487)+1,000 (0.751)

= 298.44 + 751

= Rs. 1,049.44

5. A bond, whose par value is Rs. 1000, bears a coupon rate of 12 per cent payable semi-annually and has a maturity period of 3 years. The required rate of return on bond is 10 per cent. What is the value of this bond?

Semi-annual interest payable = 1,000 x 12 per cent/2= 60

Principal repayment at the end of 3 years = Rs. 1,000

The value of the bond

= 60 (PVIFA 10%/2, 6 pds) + Rs. 1,000 (PVIF 10%/2, 6 pds) =

60 (5.0746) + 1,000 (0.746) = 304.48 + 746 = 1,050.48

6. The face value of the bond is Rs. 1,000, coupon rate is 11 per cent, years to maturity is seven years. The required rate of return is 13 per cent, and then the present value of the bond is:

110 x PVIFA (13 per cent, 7) + 1,000 (PVIF 13 per cent, 7)

110(4.423)+1,000 (0.425) = 911.53

One year from now, when the maturity period will be six years, the present value of the bond will be

110 x PVIFA (13 per cent, 6) + 1,000 (PVIF 13 per cent, 6)

110 (3.998) + 1,000 (0.480) = 919.78

Similarly, when maturity period is 5, 4, 3, 2, 1 the Bond value will become 929.87, 940.14, 952.71, 966.48, 982.35, respectively.