Question

1) You are saving $200 today. The compounding interest rate is 3%. What will your saving be after 8 years? 

2) A perpetuity of $1,000 per year beginning paying 3 years from today offers an 12% return. What is its present value? 

3) What is the present value of a 6.year annuity of S100 per year that makes its first payment 1-year from today if the discount rate is 9%? 

Answer 1

Ans 1) PV $200, Rate (r) = 3%, Time (n) = 8Years, FV = ?

FV = 200 (1+0.03)^8

FV = 200 * 1.2667

FV = $ 253.35

Ans 2)

Value of perpetuity 3 years from today

Value of perpetuity 3 years from today = Amount / Rate

Value of perpetuity 3 years from today = 1000 / 0.12

Value of perpetuity 3 years from today = $ 8333.33

Present value of perpetuity ( Assuming 12% Discount Rate)

FV = $ 8333.33, Rate 12%, Tenure (n) = 3 Years PV = ?

PV = 8333.33/(1+0.12)^3

PV = 8333.33/ 1.4049

PV = $ 5931.502

Ans 3) Future Value of annuity starting 1 Year from today

Amount = $ 100, Rate = 9%, Tenure (n-1) = 5, FV of Annuity after 6 years from now = ?

  

(The annuity will start after 1 Year for 6 years from now, so n is taken as 6-1 = 5

FVA = 100 [(1.09^5) -1] / 0.09

FVA = 100 * 5.9847

FVA = $ 598.47

Present Value of FVA :

PV = 598.47/ (1.09)^1

PV = $ 549.05