MATA32H3 Lecture Notes - Lecture 2: Annual Percentage Rate, Compound Interest, Savings Account

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MATA32H3 Full Course Notes

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Example 2. 1: suppose that is invested at the rate of 8% compounded annually. Notes: annual rate nominal rate annual percentage rate interest rate, compound amount s. Example 2. 5: you have a choice of two banks. One bank pays interest at 5. 54% interest compounded monthly and the other bank is pays interest at 5. 53% compounded daily (365 times a year). Let p be the value of the investment at time 0, Example 2. 6: a trust fund for a child"s education is being set up by a single payment so that at the end of 14 years there will be ,000. Example 2. 7: suppose that you have the opportunity to invest in a friend"s business such that you will be repaid in six years. Example 2. 8: a debt of ,000 due to 10 year from now, is instead to be paid off by two payments: now and a final payment at the end of 10 years.

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Independent parts

a- Calculate the present value (P0 =?) of $6,500 to be received in two yearsâ time when the discount rate is 8% per annum, compounded annually.

b- $700 is invested at nominal interest rate of 6% per annum. Calculate the amount due (Pt =?) at the end of 7 years if interest is compounded semiannually. c- Calculate the annual rate of interest (i =?) required for $10,000 to become $80,000 in 15 years. Assume quarterly compounding.

d- A bank pays 8% interest compounded annually. Calculate the number of years (t =?) it will take for $100,000 to grow to its doubled value? e- A family wants to start a child education plan to pay for their daughterâs university tuition in 18 years.

The total 4-year tuition will cost $100,000. They have $10,000 to invest now at a continuously compounded interest rate,

i. Find i. If a bank is willing to give them a rate of 10% compounded continuously, will it suffice?

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1. Using Table 1---Find the Future Value of $5,000 at 6% interest compounded semi-annually for 2 years.

$5,627.55

$5.835.64

$5,527.55

$5,735.64

2.Using Table 2---Find the Compound Interest on $2,500 at .75% interest compounded daily by Leader Financial Bank for 20 days.

$1.02

$10.30

$1.03

$6.31

3.Using Table 3---Find the amount of money that needs to be invested in order to have $1,500 in 3 years if you would receive 2.5% interest compounded annually.

$1,376.45

$1,403.56

$1,259.35

$1,392.90

4.Using Table 1---Find the Future Value of a $7,000 investment at 2% interest compounded semi-annually for 6 years.

$7,877.68

$9,887.81

$7,887.81

$8,877.68

5.Using Table 2---How much Compound Interest is earned on a deposit of $1,500 at .5% interest compounded daily for 30 days.

$0.62

$3.69

$0.61

$0.90

Using Table 3---Find the amount of money that needs to be invested in order to have $4,000 in 2 years if you would receive 2% compounded quarterly.

$3,589.78

$3,712.34

$3,843.56

$3,413.96

Using Table 1---Find the Future Value of a $1,000 loan at 12% interest compounded monthly for 2 years.

$269.73

$1,324.56

$1,269.73

$324.56

Using Table 2---Find the Compound Interest for John McCormick. He can invest $8,000 at .5% interest for 15 days compounded daily.

$1.65

$2.75

$2.64

$1.64

Using Table 3---Find the amount of money that needs to be invested in order to have $1,800 in 1 year if you would receive 6% interest compounded monthly.

$1,695.44

$1,398.70

$1,595.45

$1,8.34.29

Using Table 1---Find the Future Value of $18,500 at 6% interest compounded quarterly for 4 years.

$23,476.32

$21,998.97

$22,668.33

$21,675.88

Using Table 2---Find the Compound Interest on $8,000 at 1.25% interest for 180 days if it is compounded daily.

$58.46

$49.46

$49.47

$48.49

Using Table 3---Find the amount of money that needs to be invested in order to have $4,000 in 4 years if you would receive 6% interest compounded quarterly.

$2,834.67

$3,315.21

$2,476.32

$3,152.12

Using Table 1---Find the Future Value of a $10,000 investment that is invested for 5 years at 4% interest compounded semi-annually.

$12,665.89

$12,189.90

$12,912.54

$10,189.90

Using Table 2---Find the Compound Interest on $2,000 at .75% interest compounded daily for 21 days.

$0.86

$1.06

$1.86

$0.76

Using Table 3---Find the amount of money that needs to be invested in order to have $2,000 in 5 years if you would receive 3% interest compounded semi-annually.

$1,9121.25

$1,723.34

$1,599.78

$1,898.51

Using Table 1---Find the Future Value of a $3,000 investment at 3% interest compounded semi-annually for 5 years.

$2,968.12

$3,481.62

$2,986.12

$3,418.62

Using Table 2---Find the Compound Interest on $5,000 at 2.5% interest compounded daily for 120 days.

$45.25

$41.26

$40.26

$41.25

Using Table 3---Find the amount of money that needs to be invested in order to have $700 in 6 years if you would receive 6% interest compounded quarterly.

$489.68

$409.68

$389.65

$498.59

Using Table 3---Dereck Anderson plans to buy a house in four years. He will make an $8,000 down payment on the property. How much should he invest today at 6% interest compounded quarterly to have the required amount in four years?

$8,000.00

$6,304.24

$7,354.78

$6,504.24

Using Table 1---If you were offered $600 today or $680 in one year; whichwould you accept if the $600 can be invested at 6% interest compounded semi-annually?

Neither amount

$600.00

$674.16

$680.00

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MATA32H3 Lecture Notes - Lecture 2: Annual Percentage Rate, Compound Interest, Savings Account

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