Question

Courtney Cox has $10,000 that she can deposit in any of three savings accounts for a 3-year period.
Bank A compounds interest on an annual basis, Bank B compounds interest twice each year, and bank C compounds interest each quarter. All three banks have a stated annual interest of 4%.

1) What amount would Ms. Cox have at the end of the third year, leaving all interest paid on deposit, in each bank?
2) What effective annual rate (EAR) would she earn in each of the banks?
3) Based on your findings in Questions 1 and 2, which bank should Ms. Cox deal with? Why?
4) If a fourth bank (Bank D), also with a 4% stated interest rate, compounds interest continuously, how much would Ms. Cox have at the end of the third year? Does this alternative change your recommendation in Question 3? Explain why or why not.

Answer 1

1)

future value = present value(1+r)^n

where r = rate per period

n = number of periods

Bank - A:

here r = 4%

n = 3

future value = 10,000*(1+4%)^3

= $11,248.64

Bank - B:

here r = 4 / 2 = 2%

n = 3*2 = 6

future value = 10,000*(1+2%)^6

= $11,261..62

Bank - C:

here r = 4 / 4 = 1%

n = 3 x 4 = 12

future value = 10,000*(1+1%)^12

= $11,268.25

2)

EAR = (1 + r/n)^n - 1

where r = rate of return and n = number of compoundings per year

Bank A = 4%

Bank B = (1 + 4% / 2)^2 - 1

= (1.02)^2 - 1

= 4.04%

Bank C = (1 + 4%/4)^4 - 1

= 4.0604%

3)

clearly she should invest in Bank C because it gives highest return .

4)

formula for continuous compounding = P*e^r*t

where , P = 10,000

r = 4%

t = 3 years

future value = 10,000*e^0.04*3

= 10,000 * 3.320117

= $33,201.17

yes , now she should invest in Bank D as it componds continuously and gives highest return.