Ms. Watson has $100,000 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 rate of 4 percent. a) What amount
would Ms. Watson have at the end of the third year-including interest? b) What
effective interest rate would she earn at each bank? c) On the basis of your
finding in a and b, which bank should Ms. Watson deal with? Why?
The formula is
A = P(1 + r/n)^(nt)
A = 100000, r = .04, t = 3
A = 100000(1 + .04/n)^(n*3)
a) What amount would Ms. Watson have at the end of the third year-including interest.
For Bank A, n = 1,
A = 100000(1 + .04/1)^(1*3) = $112486
For Bank B, n = 2,
A = 100000(1 + .04/2)^(2*3) = $112616
For Bank C, n = 4,
A = 100000(1 + .04/4)^(4*3) = $112683
b) What effective interest rate would she earn at each bank?
I = Prt
r = I/(Pt)
For Bank A, r = 12486/(100000*3) = .04162 or about 4.162%
For Bank B, r = 12616/(100000*3) = .04205 or about 4.205%
For Bank C, r = 12683/(100000*3) = .04228 or about 4.228%
On the basis of your finding in a and b, which bank should Ms. Watson
deal with? Why?
C, because the effective interest is the greatest.
Edwin