(Interest Rate Word Problems)
1. To solve an exponential or logarithmic word problems, convert the narrative to an equation and solve the equation.
Example 3: You are trying to decide whether to deposit your $1,000 in Bank A, Bank B, Bank C, Bank D, or Bank E. You want to leave your money in the bank for 5 years and you want to maximize your ending balance.
Bank A pays 15% simple interest; Bank B pays 14% interest compounded monthly; Bank C pays 13.3% interest compounded quarterly; Bank D pays 13% interest compounded continuously; and Bank E pays 13.5% interest compounded weekly.
Which bank pays the most and which bank pays the least? In which bank will you deposit your money? What is the effective interest rate of each of the banks?
Explanation and Solution:
at the end of the five years.
The effective interest rate is the interest rate, compounded yearly, that would give you the same balance in five years
or
which gives
hence
This means that although the bank is quoting a high interest rate of 15%, in reality, the effective interest rate is only 11.84%
or
at the end of the five years.
The effective interest rate is the interest rate, compounded yearly, that would give you the same balance in five years
or
which gives
hence
This means that although the bank is quoting a 14% interest rate, in reality, the effective interest rate is a little higher at 14.93.%
at the end of the five years.
The effective interest rate is the interest rate, compounded yearly, that would give you the same balance in five years
which gives
This means that although the banks is quoting a 13.3% interest rate, in reality, the effective interest rate is a little higher at 13.98%
at the end of the five years.
The effective interest rate is the interest rate, compounded yearly, that would give you the same balance in five years
which gives
This means that although the banks is quoting a 13% interest rate, in reality, the effective interest rate is a little higher at 13.88%
or
at the end of the five years.
The effective interest rate is the interest rate, compounded yearly, that would give you the same balance in five years
which gives
This means that although the banks is quoting a 13.5% interest rate, in reality, the effective interest rate is a little higher at 14.43%
To recap: The effective interest rates of Banks A, B, C, D, and E are: 11.84%, 14.93%, 13.98%, 13.88%, and 14.43%, respectively. It appears that Bank B pays the most and Bank A pays the least.
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Author: Nancy Marcus