Part A: Present Value and Future Value Brian Inc. estimates that it will need $2

Question

Part A:

Present Value and Future Value

Brian Inc. estimates that it will need $245,000 in 6 years to expand its manufacturing facilities. A bank has agreed to pay Brian 5% interest compounded annually if the company deposits the entire amount now needed to accumulate $245,000 in 6 years.

Use the appropriate present or future value table:

FV of $1, PV of $1, FV of Annuity of $1 and PV of Annuity of $1

Required:

How much money does Brian need to deposit now? Be sure to use all digits shown on the table and round your answer to a whole dollar?

Part B:

Present Value and Future Value

The following situations require the application of the time value of money:

Use the appropriate present or future value table:

FV of $1, PV of $1, FV of Annuity of $1 and PV of Annuity of $1

1. On January 1, 2016, $14,500 is deposited. Assuming an 8% interest rate, calculate the amount accumulated on January 1, 2021, if interest is compounded (a) annually, (b) semiannually, and (c) quarterly. Round your answers to the nearest dollar.

2. Assume that a deposit made on January 1, 2016, earns 8% interest. The deposit plus interest accumulated to $26,400 on January 1, 2021. How much was invested on January 1, 2016, if interest was compounded (a) annually, (b) semiannually, and (c) quarterly? Round your answers to the nearest dollar.

Explanation / Answer

Part A:

Present value of $ 245,000 after 6 years, with 5% interest rate = 245000 / 1.056 = $ 182,822.77

Part B:

1. (a) Annual compunding:

amount accumulated on January 1, 2021 = 14500 x 1.085 = $ 21,305.26

(b) Semi-annual compounding:

amount accumulated on January 1, 2021 = 14500 x 1.0410 = $ 21,463.54

(c) Quarterly compunding:

amount accumulated on January 1, 2021 = 14500 x 1.0220 = $ 21,546.24

2. (a) Annual Compunding:

A maturity value of $ 26,400 has a present value = 26400 / 1.085 = $ 17,967.40

(b) Semiannual compounding:

A maturity value of $ 26,400 has a present value = 26400 / 1.0410 = $ 17,834.89

(c) Quarterly Compounding

A maturity value of $ 26,400 has a present value = 26400 / 1.0220 = $ 17,766.44

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