Find the periodic payments necessary to accumulate the amount of $11500 in a fund paying 5% per year, with monthly payments for 6 years. ( Assume...

To determine the periodic payment, apply the formula of future value of annuity.

`FV = (PMT[(1+r/n)^(nt)-1])/(r/n)`

where

FV is the future value

r is the rate

n is the number of payments in a year, and

t is the number of years.

The given future value is FV = 11500. The rate is r=5%. Since it is paid monthly for 6 years, then  n=12 and t=6.

Plugging them to the formula yields:

`11500=(PMT[(1+0.05/12)^(12*6)-1])/(0.05/12)`

`11500=PMT*83.76425859`

`11500/83.76425859=PMT`

`137.2900589=PMT`

Rounding off to nearest hundredths, it becomes 137.29 .

Therefore, the monthly payment should be $137.29 in order to have $11500 in 6 years.