Question

3. What is the annual interest rate that would cause $200 to grow to $289 in 8 years?

4. What is the future value of a 6-year, $203 ordinary annuity if the annual interest rate is 5%?

5. What is the PV of a 6 year, $289 annuity due if the annual interest rate is 5%?

6. What is the value of a perpetuity that makes a payment of $155 per year? Assume the current interest rate is 4%.

7. What is the PV of a 6 year, $870 ordinary annuity if the annual interest rate is 5%?

8. What is the PV of 1,570 to be received in 5 years if the interest rate is 3%, annual compounding?

Answer 1

Quesiton 3:

PV = Present Value = $200

FV = Future Value = $289

n = 8 years

Let r = annual interest rate

FV = PV * (1+r)^n

$289 = $200 * (1+r)^8

(1+r)^8 = 1.445

1+r = 1.04708872

r = 0.04708872

Therefore, annual interest rate is 4.71%

Quesiton 4:

P = Annual payment = $203

n = 6 years

r = annual interest rate = 5%

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

= $203 * [(1+5%)^6 - 1] / 5%

= $203 * 0.34009564 / 0.05

= $1,380.7883

Therefore, future value of ordinary annuity is $1,380.79

Question 5:

P = Annual payment = $289

n = 6 years

r = annual interest rate = 5%

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

= $289 * [1 - (1+5%)^-6] / 5%

= $289 * 0.253784603 / 0.05

= $1,466.87501

Therefore, present value of ordinary annuity is $1,466.88

Question 6:

Annual Payment = $155

Interest rate = 4%

Value of Perpetuity = Annual Payment / Interest rate

= $155 / 0.04

= $3,875

Therefore, value of perpetuity is $3,875

Quesiton 7:

P = Annual payment = $870

n = 6 years

r = annual interest rate = 5%

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

= $870 * [1 - (1+5%)^-6] / 5%

= $870 * 0.253784603 / 0.05

= $4,415.8521

Therefore, Present Value of Ordinary annuity is $4,415.85

Question 8:

FV = Amount to be received = $1,570

n = 5 years

r = interest rate = 3%

Present Value = FV / (1+r)^n

= $1,570 / (1+3%)^5

= $1,570 / 1.15927407

= $1,354.2958

Therefore, PV is $1,354.30