7.3 Present Value
Chapter
Chapter 7
Section
7.3
Solutions 15 Videos

Determine the present value of each h future amount for the vine conditions.

In 5 years, an investment earning 5% per year, compounded annually, will have a value of $700. Buy to View 0.24mins Q1a Determine the present value of each n future amount for the given conditions. In 3 years, an investment earning 4.8% annual interest, compounded quarterly, will have a value of$1021.86.

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Q1b

In 4 years, an investment will be worth $506.99. If interest is earned at a rte of 6% per year, compounded annually, what is the present value o this investment? Buy to View 0.24mins Q2 In 6 years, money invested 7.5% per annum, compounded quarterly, will grow to$807.21.

(a) How much money was invested?

(b) How much interest will be earned in 6 years?

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Q3

Patricia receives a financial gift from her grandparents, which she invests at 8\% annual interest, compounded semi-annually. She is advised that the investment will be worth \$3421.40 in 4 years. (a) What is the amount of the gift? (b) How much interest will Patricia's investment earn? Buy to View 1.15mins Q4 A bond will be worth$500 when it becomes due in 5 years. If the bond was purchase today for $450 at 2.13% per year, determine how frequently the interest was compounded. Buy to View 2.07mins Q5 Serge invests$700 at 5.75% per year, compounded quarterly. When the amount is closed, its value will be $950. How long will Serge's money be invested? Buy to View 1.31mins Q6 Tracey would like to have$10000 in 4 years to use as a down payment for house. She is considering two investment options:

Investment A: 6.6% annual interest, compounded semi-annually.

Investment B: 6.2% annual interest, compounded monthly.

• (a) Compare the present values of the two options.
• (b) Which investment is the better choice for Tracey? Explain your reasoning.
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Q7

Jacques needs to borrow money to buy dress clothes for his new sales job. He estimates that he can repay $1600 in 6 months. He is considering tow bank offers: Bank A 8.5% annual interest, compounded monthly Bank B 9% simple interest. Which is a better option? Buy to View 1.36mins Q8 Five years ago, money was invested at 7% per year, compounded annually. Today the investment is worth$441.28.

(a) How much money was originally invested?

(b) How much interest was earned?

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Q9

Four and a half years ago, some money was deposited into an account that paid an annual interest rate of 3.2%, compounded semi-annually. Today, the account has a value of $821.36. What was the amount of the original deposit? Buy to View 0.48mins Q10 Lynda borrows$500 to buy a television. She agrees to repay $610 in a year and a half. What annual rate of interest, compounded monthly, is Lydia being charged? Buy to View 1.20mins Q11 The future value of a lan due to a financial institution in 10 years is$50 000. The financial institution is willing to sell the debt today discounted at 6% per year, compounded semi-annually. What is the value of the debt today?

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Q14

Use algebraic reasoning to develop a formula for the present value, PV, of a simple interest account, in terms of its future value, FV; the simple annual rate of interest, r; and time, t, in years.

A debt can be paid off in three equal instalments: $1000 now,$1000 in 3 years, and \$1000 in 6 years. What single payment can pay off the loan 4 years from now, if interest is 10% per annum, compounded semi-annually?