Question

Sebastopol Movie Theater will need $180,000 in 5 years to replace the seats. What deposit should be made today in an account that pays 0.8% compounded semiannually? (a) State the type. O present value of an annuity O present value O sinking fund o ordinary annuity O amortization (b) Answer the question. (Round your answer to the nearest cent.)

Answer 1

A) Facts provided in the question

Future Value needed (FV) = $180,000

Time duration = 5 years

Since the amount gets compounded semiannually,

Compounding Period (N) = 10 (5 years and 2 semi annual periods)

Rate = 0.8% (In such questions, rate provided is usually the annual rate which needs to be changed to rate as per compounding period)

Since compounding is semi-annually,

rate (i) = 0.8/100 * 1/2 = 0.004

We have to find present Value ( PV)

The formula of future Value (FV) is as Follows

FV = PV * (1+i)^N

so PV = FV / (1+i)^N

Replacing values for FV, i and N provided above

PV = 180000 / (1+0.004)^10

So PV = $172,955.898 or $172,955.90