Series of Compound Interest Techniques The following are several situations invo

Question

Series of Compound Interest Techniques

The following are several situations involving compound interest.

Required:

Using the appropriate table, solve each of the following:

(Click here to access the time value of money tables to use with this problem.)

1.Hope Dearborn invests $40,000 on January 1, 2016, in a savings account that earns interest of 8% compounded semiannually. What will be the amount in the fund on December 31, 2021?

Round your answer to two decimal places.

$

2. Ben Johnson receives a bonus of $5,000 each year on December 31. Beginning on December 31, 2016, he deposits his bonus every year in a savings account that earns interest of 12% compounded annually. What will be the amount in the fund on December 31, 2020, after he deposits his bonus received on that date?

Round your answer to two decimal places.

$

3. Ron Sewert owes $30,000 on a non-interest-bearing note due January 1, 2026. He offers to pay the amount on January 1, 2016, provided that it is discounted at 10% on a compound annual discount basis. What would he have to pay on January 1, 2016, under this assumption?

Round your answer to two decimal places.

$

4. June Stickney purchased an annuity on January 1, 2016, which, at a 12% annual rate, would yield $6,000 each June 30 and December 31 for the next 6 years. What was the cost of the annuity to Stickney?

Round your answer to two decimal places.

$

5. Five equal annual contributions are to be made to a fund, with the first deposit on December 31, 2016. Determine the equal contributions that, if invested at 10% compounded annually, will produce a fund of $30,000 on December 31, 2021.

Round your answer to two decimal places.

$

6. Beginning on December 31, 2017, 6 equal annual withdrawals are to be made. Determine the equal annual withdrawals if $11,000 is invested at 10% interest compounded annually on December 31, 2016.

Round your answer to two decimal places.

$

Explanation / Answer

Requirement 1:

Given data,

Present Value = $40000

Number of years = 6 years

Interest Rate = 8%

Number of Conversions = 2

Applicable Rate, i = 8/2 = 4%

Period, n = 6 *2 = 12

Formula:

Present Value = Future Value *PVIF (i, n)

Future Value = $40000 / PVIF (4%, 12)

Present Value = $40000 / 0.624597

Present Value = $64041.29

Requirement 2:

Given data,

Annuity = $5000

Number of years = 4 years

Interest Rate = 12%

Number of Conversions = 1

Applicable Rate, i = 12%

Period, n = 4 *1 = 4

Formula:

Future Value = Annuity *FVAF (i, n)

Future Value = $5000 * FVAF (12%, 4)

Future Value = $5000 * 4.7793

Future Value = $23896.64

Requirement 3:

Given data,

Future Value = $30000

Number of years = 10 years

Interest Rate = 10%

Number of Conversions = 1

Applicable Rate, i = 10%

Period, n = 10*1 = 10

Formula:

Present Value = Future Value *PVIF (i, n)

Present Value = $30000 * PVIF (10%, 10)

Present Value = $30000 * 0.385543

Present Value = $11566.30

Note: Time doesnt permit me to answer the remaining questions

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