Compare Interest Rates Bank 1 Bank 2 Annual rate of interest: 2.7 2.69 Determine Number of compounding periods: 2 52 Best Bank APY: 2.718 % 2.726 % Best bank: Bank 2
Interest Rates Savings accounts state an interest rate and a compounding period. If the
amount deposited is P, the stated interest rate is r, and interest is compounded m times
per year, then the balance in the account after one year is P⋅(1+rm)m. For instance, if
$1000 is deposited at 3% interest compounded quarterly (that is, 4 times per year), then
the balance after one year is
1000⋅(1+.034)4=1000⋅1.00754=$1,030.34.
Interest rates with different compounding periods cannot be compared directly.
The concept of APY (annual percentage yield) must be used to make the comparison. The
APY for a stated interest rate r compounded m times per year is defined by
APY=(1+rm)m−1.
(The APY is the simple interest rate that yields the same amount of interest after one
year as the compounded annual rate of interest.) Write a
rates offered by two different banks and determine the most favorable interest rate. See
Fig. 4.24.
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