Repost. Not answered. Compounding frequency and time value You plan to invest $2

Question

Repost. Not answered.

Compounding frequency and time value You plan to invest $2,000 in an individual
retirement arrangement (IRA) today at a nominal annual rate of 8%, which is expected
to apply to all future years.

a. How much will you have in the account at the end of 10 years if interest is compounded
(1) annually, (2) semiannually, (3) daily (assume a 365-day year), and
(4) continuously?
b. What is the effective annual rate (EAR) for each compounding period in part a?
c. How much greater will your IRA balance be at the end of 10 years if interest is
compounded continuously rather than annually?
d. How does the compounding frequency affect the future value and effective annual
rate for a given deposit? Explain in terms of your findings in parts a through c.

Explanation / Answer

Calculation of Future value at the end of 10 years:

1) If interest is compounded annually:

Future value   = Present value * (1+r)^n

Present value   =2000

r= rate of interest = 8% = 0.08

n = number of year = 10

Hence ,

Future value   = 2000 * (1+0.08)^10

= 2000 * 2.158925

= $4317.85

2) If interest is compounded Semi-annually:

Future value   = Present value * (1+r)^n

Present value   =2000

r= rate of interest = 8%/2 = 0.04

n = number of semiannual = 10*2= 20

Hence ,

Future value   = 2000 * (1+0.04)^20

= 2000 * 2.1911231

= $ 4,382.25

3) If interest is compounded Daily:

Future value   = Present value * (1+r)^n

Present value   =2000

r= rate of interest = 8%/365 = 0.0002192

n = number of days = 10*365= 3650

Hence ,

Future value   = 2000 * (1+0.0002192)^3650

= 2000 *       2.22552

=     $ 4,451.05

4) If interest is compounded continuously:

Future value = Pe ^rt

P = Present value = 2000

e = constant value= 2.718

r= rate of interest = 8% = 0.08

t= years   = 10

Future value = 2000*(2.718 ^(0.08*10))

= 2000*2.2253563

= $ 4,450.71

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