You$$ve decided to buy a house that is valued at $$1$ million. You have $$100,000$ to use as a down payment on the house, and want to take out a mortgage for the remainder of the purchase price. Your bank has approved your $$900,000$ mortgage, and is offering a standard $30-$year mortgage at a $12\%$ fixed nominal interest rate $($called the loan$$s annual percentage rate or APR$).$ Under this loan proposal, your mortgage payment will be per month. $($Note: Round the final value of any interest rate used to four decimal places.$)$ fThe number of compounding periods in one year is called compounding frequency. The compounding frequency affects both the present and future values of cash flows.

An investor can invest money with a particular bank and earn a stated interest rate of $8\mathrm{.}80\%$; however, interest will be compounded quarterly. What are the nominal, periodic, and effective interest rates for this investment opportunity Another bank is also offering favorable terms, so Rahul decides to take a loan of $The number of compounding periods in one year is called compounding frequency. The compounding frequency affects both the present and future values of cash flows.

An investor can invest money with a particular bank and earn a stated interest rate of $8\mathrm{.}80\%$; however, interest will be compounded quarterly. What are the nominal, periodic, and effective interest rates for this investment opportunity?$14,000$ from this bank. He signs the loan contract at $9\%$ compounded daily for four months. Based on a $365-$day year, what is the total amount that Rahul owes the bank at the end of the loan's term? $($Hint: To calculate the number of days, divide the number of months by $12$ and multiply by $365.)$

$$15,292\mathrm{.}02$

$$14,714\mathrm{.}96$

$$14,931\mathrm{.}36$

$$14,426\mathrm{.}43$ Rahul needs a loan and is speaking to several lending agencies about the interest rates they would charge and the terms they offer. He particularly likes his local bank because he is being offered a nominal rate of $8\%.$ But the bank is compounding bimonthly $($every two months$).$ What is the effective interest rate that Rahul would pay for the loan?

$8\mathrm{.}356\%$

$8\mathrm{.}271\%$

$8\mathrm{.}392\%$

$8\mathrm{.}585\%$

Debbie has been donating $10\%$ of her salary at the end of every year to charity for the last three years. Her salary increased by $15\%$ every year in the last three years.

You deposit a certain equal amount of money every year into your pension fund.

Amit receives quarterly dividends from his investment in a high$-$dividend yield, index exchange$$traded fund.

Aakash borrowed some money from his friend to start a new business. He promises to pay his friend $$2,650$ every year for the next five years to pay off his loan along with interest. A series of cash flows may not always necessarily be an annuity. Cash flows can also be uneven and variable in amount, but the concept of the time value of money will continue to apply.

Consider the following case:

The Purple Lion Beverage Company expects the following cash flows from its manufacturing plant in Palau over the next five years:

Annual Cash Flows

Year $1$

Year $2$

Year $3$

Year $4$

Year $5$

$$250,000$ $$37,500$ $$480,000$ $$300,000$ $$550,000$

The CFO of the company believes that an appropriate annual interest rate on this investment is $4\%.$ What is the present value of this uneven cash flow stream, rounded to the nearest whole dollar?

$$1,410,275$

$$1,650,000$

$$2,167,500$

$$767,500$

Which of the following are characteristics of a perpetuity? Check all that apply.

The principal amount of a perpetuity is repaid as a lump$-$sum amount.

In a perpetuity, returns$$in the form of a series of identical cash flows$$are earned.

A perpetuity continues for a fixed time period.

A perpetuity is a series of regularly timed, equal cash flows that is assumed to continue indefinitely into the future. A local bank$$s advertising reads: $$Give us $$20,000$ today, and we$$ll pay you $$400$ every year forever.$$ If you plan to live forever, what annual interest rate will you earn on your deposit?

$3\mathrm{.}20\%$

$1\mathrm{.}80\%$

$1\mathrm{.}60\%$

$2\mathrm{.}00\%$

Oops! The bank representative just reported that he misquoted the available interest rate on the scholarship$$s account. Your account should earn $3\mathrm{.}50\%.$ The amount of your required deposit should be revised to $.$ This suggests there is relationship between the interest rate earned on the account and the present value of the perpetuity.Your grandfather wants to establish a scholarship in his father$$s name at a local university and has stipulated that you will administer it$.$ As you$$ve committed to fund a $$25,000$ scholarship every year beginning one year from tomorrow, you$$ll want to set aside the money for the scholarship immediately. At tomorrow$$s meeting with your grandfather and the bank$$s representative, you will need to deposit $($rounded to the nearest whole dollar$)$ so that you can fund the scholarship forever, assuming that the account will earn $5\mathrm{.}50\%$ per annum every year.