Question

(a) For an interest rate of 6% per annum compounded quarterly, determine (i) the annual effective interest rate, (ii) the effective rate per quarter, and (iii) the effective rate per month.

(b) Using the interest rates (i), (ii), and (iii) calculated in part a), calculate the future value of $1,000 deposit after 5 years.

(c) Using the interest rates (i), (ii), and (iii) calculated in part a), calculate the present value of $1,000 allowance you receive 5 years from now.

Answer 1

a.

i = 6% compounded quarterly = 6% / 4 = 1.5% per quarter

i) annual effective interest rate = (1+0.015)^4 -1

= 1.015^4 -1

= 1.06136355 - 1

= 0.06136355

= 6.1364%

ii) Effective int rate per quarter = 1.5%

iii) effective interset rate per quarter = = (1+ interest rate per month)^3 -1

(1+ interest rate per month)^3 -1 = 0.015

(1+ interest rate per month)^3 = 1.015

interest rate per month = 1.015^(1/3) - 1 = 1.00497521 - 1 = 0.00497521 = 0.497521%

b)

No of months in 5 yrs = 5*12 = 60 months

No. of quarters in 5 yrs = 5 * 4 = 20 quarters

Future value of 1000 after 5 yrs = 1000 * (1+0.06136355)^5 = 1000 * 1.346855 = 1346.86

Future value of 1000 after 20 quarters = 1000 * (1+0.015)^20 = 1000 * 1.346855 = 1346.86

Future value of 1000 after 60 months = 1000 * (1+0.00497521)^60 = 1000 * 1.346855 = 1346.86

C)

No of months in 5 yrs = 5*12 = 60 months

No. of quarters in 5 yrs = 5 * 4 = 20 quarters

Present value of 1000 received after 5 yrs = 1000 / (1+0.06136355)^5 = 1000 / 1.346855 = 742.47

Present value of 1000 received after 20 quarters = 1000 / (1+0.015)^20 = 1000 / 1.346855 = 742.47

Present value of 1000 received after 60 months = 1000 / (1+0.00497521)^60 = 1000 / 1.346855 = 742.47