An agency wants to have $100,000,000 at the end of 25 years. The agency will deposit...

An agency wants to have $100,000,000 at the end of 25 years. The agency will deposit $1,500,000 at the end of each year for 25 years. At what annual interest rate per year compounded annually, the deposits must be invested to have the ammount required at the end of year 20. Show all steps.

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Solutions

Expert Solution

We require an amount of $100,000,000 (future value) at the end of 25 years (n) by depositing $1,500,000 (annuity) at the end (ordinary annuity) of each of those years. Future value of an ordinary annuity is computed as follows -

FV = A * FVIFA (rate, 25)

or, $100,000,000 = $1,500,000 * FVIFA (rate,25)

or, FVIFA (rate , 25) = 66.6666666666 or 66.667

Now, we refer the future value interest factor annuity (FVIFA) of $1 table or sinking fund table in the 25th year and get -

At 7%, factor = 63.249

at 8%, factor = 73.106

Our rate lies betwen the two as our factor lies between the two. It would be higher than 7% but less than 8% , so we need to interpolate -

Difference required = 66.667 - 63.249 = 3.418

Total difference = 73.106 - 63.249 = 9.857

Rate of interest = Lower rate + Difference in rates x ( Difference required / Total difference)

or, Rate of interest = 7% + 1% x (3.418 / 9.857) = 7.346759% or 7.35%

Let me know in case you have any issues in the comments.

jeff jeffy answered 1 year ago

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