$12$A MATH $90---$ Mathematics of Finance

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Question $1$

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A series of payments $($usually of equal size$)$ made at equal time intervals is known as a$($ or an$)$:

a$.$

cash flow

b$.$

present value

c$.$

discount

d$.$

annuity

e$.$

future value

Question $2$

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You wish to determine the equivalent value of a payment or stream of payments at a chosen point of reference. To help your calculation, you visually represent the situation by using the following timeline.

$500050005000500050005000$ stream of payments

$|---------|----------|----------|----------|----------|----------|$

Yr$0$ Yr$1$ Yr$2$ Yr$3$ Yr$4$ Yr$5$ Yr$6$

Timeline

$$

Focal Date

What is shown above is the

a$.$

future value of a lump sum

b$.$

present value of a lump sum

c$.$

future value of an ordinary annuity

d$.$

present value of a perpetuity

e$.$

present value of an ordinary annuity

Question $3$

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Which of the following problems can be solved using the present value of annuity tool introduced in this class?

a$.$

Scottie wants to accumulate $$30,000$ for a down payment for a house. He can only afford to set aside $ $300$ at the beginning of every month. The account will credit interest monthly at the annual rate of $7\mathrm{.}5\%.$ How long will it take Scottie to reach his goal?

b$.$

You have decided to put $ $200$ in a savings account on the first of every month for $10$ years. The savings account credits interest monthly, at the annual rate of $6\%.$ How much money will you have in your account immediately after your last deposit?

c$.$

Pascal has recently opened an RRSP$.$ He plans to deposit $$190$ at the end of every month for $15$ years. The account will compound interest monthly at the annual rate of $9\%.$ How much money will Pascal have in your account immediately after your last deposit?

d$.$

Amanda would like to accumulate $$52,000$ for a down payment on a house. She has decided to make deposits on the first of every month in a savings account that pays $6\%$ annual interest, compounded monthly. If Amanda wishes to reach her goal in $5$ years, how much should her monthly payment be$?$

e$.$

Sherry has taken a mortgage of $ $200,000.$ She can only afford to make monthly payments of $$6000.$ How long will it take Sherry to repay a mortgage if the bank charges $6\%$ interest annually on this mortgage