Question

The present value of A dollars to be paid t years in the future (assuming a 5% continuous interest rate) is P(A, t) = Ae-0.051. Find and interpret P(100, 13.8).

Answer 1

Present Value of A Dollars P(A,t) = Ae^(-0.05*t)

here, 100 represents the future value

and, 13.8 represents the time t

This means that at time t = 13.8 years

we received Amount A = 100

SO the PV of this Future amount A today at contnuous rate of interest of 5% would be

So, P(100,13.8)= 50.16 =100*EXP(-0.05*13.8)

Cross check :-

Now if we have to find it's Fture value i.e. how much we will have if we invest it at 5 % continuous compounded rate

Future Value (100,13.8) = 100 =C10*EXP(0.05*13.8)

So our solution is correct.