Question

1) An investment is made at rate 4.50% continuously compounded for 10 years. How much is the future value, if the initial investment is $1,000? $________

a)"1,575"

b)"1,568"

c)"1,540"

d)"1,535"

2) You plan to invest for 3.5 years. At what continuously compounded interest rate will your money double? _____%

a)19.81

b)20

c)18.73

d)19.5

3)How much is the future value of $1,000 payments made every 2 years for 40 years. The 1-year (APR) interest rate 8%.

a)124,546"

b)"259,057"

c)"114,405"

d)"74,445"

4) How much is the present value of receiving payments of $2,500 every two years for 18 year with interest rate 5.00%?"

a)"17,770"

b)"29,224"

c)"14,256"

d)"11,610"

Answer 1

Question 1:

Initial Investment = $1,000

r = interest rate = 4.5%

t = 10 years

Future Value = Initial Investment * e^(r*t)

= $1,000 * e^(4.5%*10)

= $1,000 * 1.56831219

= $1,568.31219

Therefore, Future value if $1,568

Question 2:

Present Value = $1

Future Value = $2

n = 3.5 years

Future Value = Present Value * e^(r*t)

$2 = $1 * e^(r*3.5)

2 = e^(r*3.5)

r * 3.5 = log(2) / log(e)

r*3.5 = 0.301029996 / 0.434294482

r = 0.198042051

r = 19.80%

Therefore, Compound interest rate is 19.80%

Question 3:

P = Payment for 2 years = $1,000

n = 40 / 2 = 20 periods

r = 2 year interest rate = (1+8%)^2 - 1 = 0.1664 = 16.64%

Future Value = P * [(1+r)^n - 1] / r

= $1,000 * [(1+16.64%)^20 - 1] / 16.64%

= $1,000 * 20.7245215 / 0.1664

= $124,546.403

Therefore, Future Value if $124,546

Question 4:

P = Payment for 2 years = $2,500

n = 18 / 2 = 9 periods

r = 2 year interest rate = (1+5%)^2 - 1 = 0.1025 = 10.25%

Present Value of payments = P * [1 - (1+r)^-n] / r

= $2,500 * [1 - (1+10.25%)^-9] / 10.25%

= $2,500 * 0.584479345 / 0.1025

= $14,255.5938

Therefore, Future value is $14,256