$1.$ Future Values of Lump Sums and Annuities

Use the future value table to help answer the following time value of money questions.

Future Value of $$1$ Future Value of an Ordinary Annuity

r $=2\%$ r $=5\%$ r $=2\%$ r $=5\%$

n $=01\mathrm{.}00001\mathrm{.}00000\mathrm{.}0000\mathrm{.}000$

n $=11\mathrm{.}02001\mathrm{.}05001\mathrm{.}0001\mathrm{.}000$

n $=21\mathrm{.}04041\mathrm{.}10252\mathrm{.}0202\mathrm{.}050$

n $=31\mathrm{.}06121\mathrm{.}15763\mathrm{.}0603\mathrm{.}153$

n $=41\mathrm{.}08241\mathrm{.}21554\mathrm{.}1224\mathrm{.}310$

n $=51\mathrm{.}10411\mathrm{.}27635\mathrm{.}2045\mathrm{.}526$

$1.$ What is the future value of $$1,000$ after $2$ years if the interest rate is $2\%?$

$2.$ What is the future value of $$1,000$ after $5$ years if the interest rate is $2\%?$

$3.$ What is the future value of $$1,000$ after $5$ years if the interest rate is $5\%?$

$4.$ Does a higher interest rate cause the future value of a lump sum to increase or decrease?

$5.$ What is the future value of a $2-$year $$1,000$ annuity if the interest rate is $2\%?$

$6.$ What is the future value of a $5-$year $$1,000$ annuity if the interest rate is $2\%?$

$7.$ What is the future value of a $5-$year $$1,000$ annuity if the interest rate is $5\%?$

$8.$ Does a lower interest rate cause the future value of an ordinary annuity to increase or decrease?

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$2.$ Present Values of Uneven Cash Flows

A firm is trying to choose between $4$ different investments, which are summarized in the following timeline. Assume all cash flows are received at the end of the year.

Year $12345$

Cash Flow:

Investment $1$ $$60,000$

Investment $2$ $$25,000$ $$30,000$

Investment $3$ $$10,000$ $$10,000$ $$10,000$ $$10,000$ $$10,000$

Investment $4$ $$20,000$ $$20,000$ $$20,000$

Use the present value table to help calculate the present value of the $4$ investments.

Present Value Factors for r $=5\%$

n $=0$ n $=1$ n $=2$ n $=3$ n $=4$ n $=5$

PV of $$11\mathrm{.}00000\mathrm{.}95240\mathrm{.}90700\mathrm{.}86380\mathrm{.}82270\mathrm{.}7835$

PV of Annuity $0\mathrm{.}0000\mathrm{.}9521\mathrm{.}8592\mathrm{.}7233\mathrm{.}5464\mathrm{.}329$

$1.$ What is the present value of investment $1?$

$2.$ What is the total present value of investment $2?$

$3.$ What is the total present value of investment $3?$

$4.$ What is the total present value of investment $4?$

$5.$ Which investment has the largest present value?

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$3.$ Loan Amortization

A firm borrows $$25,000$ from the bank at a $12\%$ annual interest rate to purchase some new machinery. This loan is to be repaid in equal installments at the end of each year over the next $5$ years.

$1.$ If the present value factor is $3\mathrm{.}605,$ what is the annual loan payment made by the firm?

$2.$ What is the interest payment made by the firm during the first year of the loan?

$3.$ What is the principal repayment made by the firm during the first year of the loan?

$4.$ What is the loan balance at the end of the first year of the loan?

$5.$ What is the interest payment made by the firm during the second year of the loan?

$6.$ What is the principal repayment made by the firm during the second year of the loan?

$7.$ What is the loan balance at the end of the second year of the loan?

$8.$ If the loan balance is $$6,192\mathrm{.}18$ at the end of the fourth year of the loan, what annual loan payment does the firm make during the fifth year of the loan?