Question

14. Find the present value of $2000 due in three years and 8 months if money is worth 8% p.a. compounded quarterly.

15. How long does it take for money to double at 5% compounded annually.

13. Determine the amount of money that must be invested for 245 days at 5.75% to earn $42.46

Answer 1

a) PV of 2000 due in 3 yrs & 8 months @ 8% compounded quarterly

PV = FV/(1+r)^(n); n = (3*12 + 8)/4 (4 for qtrly compounding)

= 2000/(1+5%)^11

= 1169.36

b) FV=PV*(1+r)^n

FV = 2; PV=1; r=5% compounded annually; n=?

2=1*(1.05)^n

solving for n we get 14.2 yrs

Using rule of 72 the no. of years it takes to double investment = 72/intrest rate = 72/5 ~ 14.4 yrs

c) How much to be invested for 245 days at 5.75% to earn $42.46

Here I am assuming the intrest rate to be per annum and we have to earn 42.46 as total investment value after 245 days

PV = FV/(1+r)^n; r = 5.75^

= 42.46/(1+5.75%)^(245/365)

= 40.90