Question

1) a. Find the present value of an ordinary annuity if you have a plan to pay an annuity of Rial Omani B at the end of each week for A years. Bank Muscat offers the discount rate of E % compounded weekly.

b. Suppose that you have deposited Rial Omani (B × E) in the special account of Bank Nizwa at the end of each semi year for C months. If the special account of Bank Nizwa offers at the rate of ( D / E ) % compounded semiannually, then calculate the future value of an ordinary annuity.

Note for both parts

Take A = 14 , B = 2980 , C =980 , D =80 , E = 8

Answer 1

1. (a) Calculation of Present value of ordinary Annuity -

Formula of Present value of ordinary annuity = C*[1 - (1+i/m)^(-n*m)]/(i/m)

Where C - Cash flow aper period B = 2980

i - annual interest rate E = 8%

n - number of years A = 14

m - number of compounding in a year m 52 weeks

put all these values in above formula

Present value of ordinary annuity = 2980*[1 - (1+0.08/52)^(-14*52)]/(0.08/52)

= 2980*[1 - 1.001538^(-14*52)]/(0.08/52)

= 2980*[1 - 0.326561]/(0.08/52)

= 2980*[0.673439]/0.001538

= 2006.849/0.001538

= $ 1304452

1. (b) Future value of ordinary annuity = C*[(1+i/m)^(n*m) - 1]/(i/m)

Where C - Cash flow per period B*E (2980*8) = 23840

i - annual interest rate D/E% = 80/8 = 10% per annum

n - number of years C = 980/12 = 81.66 years

m - number of compounding in a year m = 2 (semi-annually)

put all the values in above formula

Future value of ordinary annuity = 23840*[(1+0.10/2)^(81.66*2) - 1]/(0.10/2)

= 23840*[1.05^(81.66*2) - 1]/(0.10/2)

= 23840*[1.05^(81.66*2) - 1]/(0.10/2)

= 23840*[2888.26 - 1]/0.05

= 23840*2887.26/0.05

= 68832284/0.05

= 1376645690

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