Question

Please provide a CFD (Cash Flow Diagram) in addition to your solution. Thank You.

Problem-4 A $10,000 bond has an interest rate of 6% per year payable quarterly. The bond matures 15 years from now. At an interest rate of 8% per year, compounded quarterly, the present worth of the bond is closest to:$------- Answer: CFD:

Answer 1

Calculation of the present worth of the bond:

Amount of interest paid per period

I = bond value *bond interest rate/number of payment periods per year

= (10,000)*6%/4

= 10,000*0.06/4

= 150

i = 8%/4

= 2%

= 0.02

n = 15 years*4(quarterly)

= 60

Calculate the present worth of the bond by using following formula:

PW = I(P/A,i,n)+FV(P/F,i,n)

= 150(P/A,2%,60)+10,000(P/F,2%,60)

(P/A,i,n) = (1+i)ⁿ-1/i(1+i)ⁿ

= (1+0.02)⁶⁰-1/0.02(1+0.02)⁶⁰

(P/A,2%,60) = 34.76

(P/F,i,n) = (1+r)^-n

= (1+0.02)^-60

= 0.30478

(P/F,2%,60) = 0.3048

PW = I(P/A,i,n)+FV(P/F,i,n)

= 150(34.76)+10,000(0.3048)

= 5214+3048

= 8262

Therefore, the present worth of the bond is 8262.