Question

Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated.PMT = $7,500, interest is 4% compounded semiannually for 2 years Round the answer to nearest cent.

Answer 1

Given data:

PMT = $7,500

Interest rate = 4% or 0.04

Compounded semiannually = twice per year

Time = 2 years

Number of periods in total = 2 years x twice per year = 4 periods

interest rate per period = 0.04/2 = 0.02

The formula in getting the future value of an ordinary annuity is:

`F=PMT((1+i)^n-1)/(i))`

where

i = interest rate per period

n = total number of periods

PMT = regular payment

From the given data above, let's substitute those in the formula.

`\begin{gathered} F=7500*((1+0.02)^4-1)/(0.02) \\ F=7500*(1.02^4-1)/(0.02) \\ F=7500*(0.08243216)/(0.02) \\ F=7500*4.121608 \\ F=30,912.06 \\ F\approx30,912.1 \end{gathered}`

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