Answered

For each of the following cases, indicate (a) the interest rate column and (b) the number of periods you would refer to in looking up the discount rate.

1. In Table 3 (present value of 1):

| Case | Annual Rate | Number of Years Invested | Discounts per Year |
|------|--------------|-------------------------|--------------------|
| A | 9% | 7 | Annually |
| B | 14% | 14 | Semiannually |
| C | 10% | 9 | Semiannually |

(a)
(b)

- Case A: ___% ___ periods
- Case B: ___% ___ periods
- Case C: ___% ___ periods

2. In Table 4 (present value of an annuity of 1):



Answer :

GinnyAnswer
To determine the correct interest rate and number of periods to refer to when looking up the discount rate for each case, we need to consider how the interest rate is compounded and the duration of the investment. Let's analyze each case in detail:

### Case A:
- Annual Interest Rate: 9%
- Number of Years Invested: 7
- Discounts per Year: Annually

Since the interest is compounded annually, the interest rate remains the same each year.

Step-by-step solution:
(a) Interest Rate: 9% (annual).
(b) Number of Periods: 7 years.

### Case B:
- Annual Interest Rate: 14%
- Number of Years Invested: 14
- Discounts per Year: Semiannually

Since the interest rate is compounded semiannually, we need to adjust both the interest rate and the number of periods.

Step-by-step solution:
(a) Interest Rate: The semiannual rate is half of the annual rate. So, the semiannual rate is 14% / 2 = 7%.
(b) Number of Periods: Since the compounding occurs semiannually, the number of periods is twice the number of years. So, the number of periods is 14 2 = 28 periods.

### Case C:
- Annual Interest Rate: 10%
- Number of Years Invested: 9
- Discounts per Year: Semiannually

Again, for semiannual compounding, we need to adjust the interest rate and the number of periods.

Step-by-step solution:
(a) Interest Rate: The semiannual rate is half of the annual rate. So, the semiannual rate is 10% / 2 = 5%.
(b) Number of Periods: Since the compounding occurs semiannually, the number of periods is twice the number of years. So, the number of periods is 9 2 = 18 periods.

### Summary for Table 3 (present value of 1):
(a)
- Case A: 9% interest rate
- Case B: 7% interest rate (semiannual)
- Case C: 5% interest rate (semiannual)

(b)
- Case A: 7 periods
- Case B: 28 periods (semiannual)
- Case C: 18 periods (semiannual)

### For Table 4 (present value of an annuity of 1):

Let's apply the same logic:

### Case A:
- Annual Interest Rate: 9%
- Number of Years Invested: 7
- Discounts per Year: Annually

### Case B:
- Annual Interest Rate: 14%
- Number of Years Invested: 14
- Discounts per Year: Semiannually

### Case C:
- Annual Interest Rate: 10%
- Number of Years Invested: 9
- Discounts per Year: Semiannually

For annuity calculations, the logic regarding interest rate and periods remains the same as with the present value of 1.

### Summary for Table 4 (present value of an annuity of 1):
(a)
- Case A: 9% interest rate
- Case B: 7% interest rate (semiannual)
- Case C: 5% interest rate (semiannual)

(b)
- Case A: 7 periods
- Case B: 28 periods (semiannual)
- Case C: 18 periods (semiannual)

In both tables (present value of 1 and present value of an annuity of 1), the relationship between the interest rates and the number of periods is the same, based on the compounding frequencies provided in the problem statement.