Question

1. You currently have AED40,000 and plans to purchase a 5-year certificate of deposit (CD).

a. How much will you have when the CD matures if it pays 7% interest, compounded annually?

b. How much will you have when the CD matures if it pays 6%, or 20% interest, compounded annually?

c. How much will you have when the CD matures if it pays 6%, or 20% interest, compounded semiannually?

d. Why does the annual compounding and semiannual compounding give different answers?

Would you prefer annual compounding or semiannual compounding or quarterly compounding for your investments?

e. How much will you have when the CD matures if you purchase a 10-year CD that pays 7% interest, compounded annually?

f. Do you observe any relationship between the period of investment and the future value?

Answer 1

a) FV = PV(1+r)^n

=40,000(1+7%)^5

=40,000(1.07)^5

=40000(1.402552)

=56102.07$

b) if Cd pays 6% , then

FV = PV(1+r)^n

=40,000(1+6%)^5

=40,000(1.06)^5

=40000(1.338226)

=53529.02$

If r = 20%, then,

FV = PV(1+r)^n

=40,000(1+20%)^5

=40,000(1.2)^5

=40000(2.48832)

=99532.8$

C) If interest is compounded annually

FV = PV(1+r)^n

=40,000(1+3%)^10

=40,000(1.03)^10

=40000(1.343916)

=53756.66$

If r = 20%, then,

FV = PV(1+r)^n

=40,000(1+10%)^10

=40,000(1.1)^10

=40000(2.593742)

=103749.7$

d) Because in semi annual compounding interest earnd for 6 month is included while calculating balance at end of year one resulting in higher future value, hence more the compounding more the interest

Hence one should prefer quarterly compounding for your investments