Solution to Example 0 on 10/8
(a) The saving account of Wells Fargo will pay the interest only once a year. So we should apply the
Compound Interest Formula
A = P × (1 + APR)Y
We will get
A = 10000 $ × (1 + 12.5%)5 = 18020.32 $
and
total interest = accumulated balance − original principal
= 18020.32 $ − 10000 $
= 8020.32 $
For Chase Bank, since the interest will be paid 12 times per year, we should use
µ
APR
A=P × 1+
n
¶(nY )
where n = 12. We will get
µ
¶(12×5)
12%
A = 10000 $ × 1 +
= 18166.97 $
12
and
total interest = accumulated balance − original principal
= 18166.97 $ − 10000 $
= 8166.97 $
To conclude, the accumulated balances in Wells Fargo and Chase Bank after 5 years are $18020.32
and $18166.97, respectively. And the interests given in this period are $8020.32 and $8166.97,
respectively. Obviously, Chase Bank will give me more interest.
(b) Recall that
µ
APY =
APR
1+
n
¶n
−1
For Wells Fargo, APR = 12.5% and n = 1, so
µ
APY =
1+
12.5%
1
¶1
− 1 = 0.125 = 12.5%
For Chase Bank, APR = 12% and n = 12, so
µ
APY =
12%
1+
12
¶12
− 1 = 0.1268 = 12.68%
From all the calculation above, we may draw the conclusion that given the same original principal
and the same total saving time, a higher APR won’t lead to a higher total interest payment, but a
higher APY will definitely lead to a higher total interest payment.