Question

How much money should be deposited today in an account that earns 5% compounded semiannually so that it will accumulate to $14,000 in three​ years?

Answer 1

First, calculate for the effective interest.

ieff = (1 + i/m)^m - 1

Substituting the known values,

ieff = (1 + 0.05/2)^2 - 1
ieff = 0.050625

Then, using the equation,

F = P x (1 + ieff)^n

Substituting,

14,000 = P x (1 + 0.050625)^3

The value of P from the equation is 12072.15612

Answer: $12,072.16