Concept explainers
Learning Goals 2, 5
ST5-1
- a. What amount would Ms. Martin have after 3 years, leaving all interest paid on deposit, in each bank?
- b. What effective annual rate (EAR) would she earn in each of the banks?
- c. On the basis of your findings in parts a and b, which bank should Ms. Martin deal with? Why?
- d. If a fourth bank (bank D), also with a 4% stated interest rate, compounds interest continuously, how much would Ms. Martin have after 3 years? Does this alternative change your recommendation in part c? Explain why or why not.
Subpart (a)
To calculate: Future value.
Introduction:
Future value (FV): The future value refers the value of present amount at a future date.
Answer to Problem 5.1STP
Bank A= $11,250
Bank B= $11,260
Bank C= $11,270
Explanation of Solution
Given:
Present value, $10,000, interest rate 4%, time period 3.
Calculation
The general formula for calculating future values is shown below.
Substitute the values in equation (1) to calculate future values of $10,000.
FV is $11,250.
By using the same equation (1), the future value of deposit $10,000 in each bank is shown below.
Table 1 shows the future value.
Table 1
Bank | Present value | Years to compound | Interest | Future value |
A | $10,000 | 3 years | 4% | $11,250 |
B | $10,000 | Two times in a year | 4% | $11,260 |
C | $10,000 | Quarterly (4) | 4% | $11,270 |
Subpart (b)
To calculate: Effective annual rate.
Introduction:
Effective annual rate (EAR): Effective annual rate refers, it is the annual rate of interest which is actually paid or earned.
Answer to Problem 5.1STP
Bank A= 4%
Bank B= 4.04%
Bank C= 4.06%
Explanation of Solution
Given:
Interest rate 4%, time period 3.
Calculation
The general formula for calculating the effective annual rate is shown below.
Substitute the values in equation (2) to calculate the EAR for deposit $10,000 in bank A.
EAR is 4%.
By using the same equation (1), the EAR for each case is shown below.
Table 2 shows the EAR.
Table 2
Bank | Years to compound | Interest | EAR |
A | 3 years | 4% | 4% |
B | Two times in a year | 4% | 4.04% |
C | Quarterly (4) | 4% | 4.06% |
Subpart (c)
To discuss: Which bank the investor will choose.
Answer to Problem 5.1STP
Bank C
Explanation of Solution
The investor will choose bank C, because, the compounding frequency is 4 (quarterly). Higher the compounding frequency increases the future value of deposit. Thus, bank C is best.
Subpart (d)
To calculate: Future value.
Introduction:
Future value (FV): The future value refers the value of present amount at a future date.
Answer to Problem 5.1STP
$11,274.97
Explanation of Solution
Given:
Present value, $10,000, interest rate 4%, time period 3.
Calculation
In bank D, the interest is compounded continuously. Calculation of future values of $10,000 with continues compounding is shown below.
The value of “e” is approximately “2.7183”.
FV is $11,274.97.
Comparing Bank D with C, bank D is better than C, because, the compounding frequency and future value obtained in bank D is higher than bank C. thus, bank D is a good alternative.
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Chapter 5 Solutions
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