Time Value of Money Future Value $\_$ Present Value

You plan to go to Asia to visit friends in three years. The trip is expected to cost a total of $$10,000$ at that time. Your parents have deposited $$5,000$ for you in a Certificate of Deposit paying $6\%$ interest annually, maturing three years from now. Uncle Lee has agreed to pay for all remaining expenses. If you are going to put Uncle Lee's gift in an investment earning $10\%$ over the next three years, how much must he deposit today, so you can visit your friends three years from today?

$$3,757$

$$3,039$

$$5,801$

$$3,345$

Although you have made no deposits or withdrawals from your emergency fund account, the account value has risen during the past $3$ years from $$15,000$ to $$17,613\mathrm{.}62.$

What has been the compound annual interest rate that has been credited to your account?

$\_\_\_\_\_\_\_\_\%$

At that rate, how many more years will be needed until your account balance reaches $$20,000?$

$\_\_\_\_\_$ years

Assume a bank loan requires an interest payment of $$1,200$ per year and a principal payment of $$20,000$ at the end of an eight$-$year life.

At what amount could this loan be sold to another bank if loans of similar quality carried a $8\mathrm{.}5\%$ interest rate? That is$,$ what would be the Present Value of this loan to the nearest dollar?

$ $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Now, if interest rates on other similar quality loans are $10\%,$ what would be the PV of his loan to the nearest dollar?

$ $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

What would be the PV of this loan if the interest rate is $6\mathrm{.}5\%$ on similar quality loans to the nearest dollar?

$ $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Which amount is worth more at $8\mathrm{.}50\%$ compounded annually: $$1,000$ in hand today or $$2,000$ due in $8$ years?

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

To the closest year, how long will it take $$35,000$ to double if it is deposited and earns $6\mathrm{.}25\%$ compounded annually to the nearest decimal point?

$\_\_\_\_\_\_\_\_\_\_\_\_$ years

If you wish to accumulate $$140,000$ in $13$ years, how much must you deposit today in an account that pays an annual interest rate of $14\%?$

What will $$247,000$ grow to be in $9$ years if it is invested today in an account with an annual interest rate of $11\%$ with quarterly compounding?

How many years will it take for $$136,000$ to grow to be $$468,000$ if it is invested in an account with an annual interest rate of $8\%$ to the nearest year?

At what annual interest rate must $$115,000$ be invested so that it will grow to be $$530,000$ in $14$ years?

If you wish to accumulate $$197,000$ in $5$ years, how much must you deposit today in an account that pays a quoted annual interest rate of $13\%$ with semi$-$annual compounding of interest?

What will $$153,000$ grow to be in $13$ years if it is invested today in an account with a quoted annual interest rate of $10\%$ with monthly compounding of interest?

How many years will it take for $$197,000$ to grow to be $$554,000$ if it is invested in an account with a quoted annual interest rate of $8\%$ with monthly compounding of interest to the nearest year?

A real estate appraiser has advised you that the value of the homes in your neighborhood has been rising at a compound annual rate of about $5\%$ in recent years. On the basis of this information, what is the value today of the house you bought $8$ years ago for $$129,500?$

$ $180,754$

$ $181,122$

$ $191,330$

$ $181,308$

How long does it take for $$5,000$ to grow into $$6,400$ at $10\%$ compounded quarterly?

$2$ years.

$3$ years.

$4$ years.

$30$ months.

What nominal annual interest rate is implied if you borrow $$12,500$ and repay $$21,364\mathrm{.}24$ in three years with monthly compounding?

$12\%$

$15\%$

$17\%$

$18\%$

Compound interest is interest earned on interest in addition to interest earned on the principal.

True

False

The future value of a dollar $\_\_\_\_\_\_\_\_$ as the interest rate increases and $\_\_\_\_\_\_\_\_$ the farther in the future is the funds are to be received.

decreases; decreases.

decreases; increases.

increases; increases.

increases; decreases

Discounting is an arithmetic process whereby a future sum decreases at a compounding interest rate over time to reach a present value.

TRUE

FALSE

Which of the following conclusions would be true if you earn a higher rate of return on your investments?

The greater the present value would be for any lump sum you would receive in the future.

The lower the present value would be for any lump sum you would receive in the future.

Your rate of return would not have any effect on the present value of any sum to be received in the future.

The greater the present value would be for any annuity you would receive in the future.

When using a financial calculator, cash outflows generally have to be entered as negative numbers, because a financial calculator sees money "leaving your hands."

TRUE

FALSE

A timeline identifies the timing and amount of a stream of cash flows, along with the interest rate it earns.

TRUE

FALSE