Question

Pharoah Company issued $1,220,000, 11-year bonds. It agreed to make annual deposits of $98,000 to a fund (called a sinking fund), which will be used to pay off the principal amount of the bond at the end of 11 years. The deposits are made at the end of each year into an account paying 9% annual interest.

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(For calculation purposes, use 5 decimal places as displayed in the factor table provided.)
What amount will be in the sinking fund at the end of 11 years? (Round answer to 2 decimal places, e.g. 25.75.)
Amount in the sinking fund
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Answer 1

The amount in the sinking fund at the end of 11 years can be calculated using the future value of an annuity formula, applying the annual deposit amount, interest rate, and number of years. The answer must then be rounded to two decimal places.

Step-by-step explanation:

To determine the amount that will be in the sinking fund at the end of 11 years, we need to calculate the future value of an annuity, which is the sum of all the deposits made into the account, each earning interest compounded annually at a rate of 9%. The formula for the future value of an annuity is given as:

FV = P * [(1 + r)^n - 1] / r

Where FV is the future value of the annuity, P is the annual deposit, r is the annual interest rate (expressed as a decimal), and n is the number of periods.

In the case of Pharoah Company, with an annual deposit P of $98,000 at an interest rate r of 9% (or 0.09), over n = 11 years, the future value FV can be calculated as follows:

FV = $98,000 * [(1 + 0.09)^11 - 1] / 0.09

After performing the calculations, we can then round the answer to two decimal places to find the amount in the sinking fund at the end of 11 years.

Answer 2

The amount in the sinking fund at the end of 11 years is $1,393,020.25

Given:

Face value of bonds = $1,220,000

Number of years (n) = 11

Annual deposit = $98,000

Interest rate (r) = 9%

Formula:

The future value of each annual deposit can be calculated using the formula:

Future value = Present value * (1 + r)^n

The total future value of the sinking fund is the sum of the future values of each annual deposit.

Calculation:

For each annual deposit, the number of compounding periods equals the years remaining until bond maturity. First deposit: 11 years, second: 10 years, and so forth

Using the formula and the factor table provided, we can calculate the future value of each annual deposit:

Year Deposit Number of Periods Future Value

1 $98,000 11 $172,090.88

2 $98,000 10 $155,335.23

3 $98,000 9 $139,365.56

4 $98,000 8 $124,138.65

5 $98,000 7 $109,635.26

6 $98,000 6 $95,856.23

7 $98,000 5 $82,812.35

8 $98,000 4 $70,425.24

9 $98,000 3 $58,707.58

10 $98,000 2 $47,577.62

11 $98,000 1 $37,041.34

Total future value = $1,393,020.25

The amount in the sinking fund at the end of 11 years is $1,393,020.25.