Question

Oven looks at his account and notices that if the current monthly interest rate stays constant he is expected to have $45,000 in 6 years (i.e. once 6 years have elapsed) and $89,000 in 9 years. (15 points) a. How much money does he have now (at time 0)?

Answer 1

Answer:

Present Value= $11,523.99

Explanation:

Giving the following information:

Oven looks at his account and notices that if the current monthly interest rate stays constant he is expected to have $45,000 in 6 years and $89,000 in 9 years.

First, we need to calculate the interest rate compounded monthly using a variation of the future value formula:

FV= PV*(1+i)^n

Isolating i:

i= [(FV/PV)^(1/n)] - 1

FV= 89,000

PV= 45,000

n= 3*12= 36

i= [(89,000/45,000)^(1/36)]-1= 0.0191

i= 0.0191*100= 1.91% compunded monthly

Now, we can calculate the present value:

PV= FV/(1+i)^n

n= 6*12= 72

i= 0.0191

PV= 45,000

PV= 45,000/(1.0191^72)

PV= 11,523.99