Question

1. Complete the chart for calculating compound interest on the amounts below.

Term	Interest Rate	Compounding Period	P	i	n	A
a. 7 years	8.5%	$6500
b. 30 days	6.5%	$890
c. 23 months	11.35%	$3000

2. Larry plans to buy his first house in 15 years. He estimates that he will need $25,000. He invented $11,550 today at &%, compounded semi-annually. Will he accomplish his goal? Explain.

3. Julie's grandmother gave her $500 for her birthday. What interest rate, compounded monthly, would she need to make $500 grow in $1250 in 10 years?

Answer 1

Question 1:

Calculating compound interest:

a.)

Time - 7 years

Interest - 8.5%

Principal - $6500

Assuming annual compounding:

Interest Amount = P*((1+r/100)^T - 1)

= 6500( (1+ 8.5/100)^7 - 1)

= 6500 (1.085^7 - 1)

= 6500 * 0.77014

= 5005.91 $

b.)

Time - 30 days

Interest - 6.5%

Principal - $890

Number of compounding periods a year - n - 365

Assuming daily compounding:

Interest Amount = P*((1+r/n*100)^T - 1)

= 890( (1+ 6.5/365*100)^30 - 1)

= 890 (1.0001781^30 - 1)

= 890 * 0.0053563

= 4.7671 $

c.)

Time - 23 months

Interest - 11.35%

Principal - $3000

Number of compounding periods a year - n - 12

Assuming monthly compounding:

Interest Amount = P*((1+r/n*100)^T - 1)

= 3000( (1+ 11.35/12*100)^23 - 1)

= 3000 (1.009458^23 - 1)

= 3000 * 0.241747

= 725.241 $

Question 2.

Time - 15 years

FV - $25000

PV - $11550

Number of compounding periods a year - n - 2

FV = P*(1+r/n*100)^T*n

25000 = 11550* (1 + &/100*2) ^ 15*2

25000/11550 = (1+ &/100*2)^ 30

2.1645^1/30 = 1+ &/200

1.026074 = 1 + &/200

0.026074 = &/200

& = 5.2148

Thus, if the interest rate of the investment is 5.2148%, it is possible.

Question 3.

Time - 10 years

FV - $1250

PV - $500

Number of compounding periods a year - n - 12

FV = P*(1+r/n*100)^T*n

1250 = 500* (1 + r/12*100)^12*10

1250/500 = ( 1+ r/1200)^120

2.5 = (1 + r/1200)^120

1.007665 = 1 + r/1200

0.007665 = r/1200

r = 9.198%

Thus the required interest rate = 9.198%