**Answer:**

He would have to save each month in years 11 through 30 the amount of $2,279.60

**Explanation:**

Because the cash flows occur monthly, we must get the effective monthly rate. One way to do this is to find the APR based on monthly compounding, and then divide by 12. So, the pre-retirement APR is:

EAR = .11 = [1 + (APR/12)] 12- 1;

APR = 12[(1.11) 1/12- 1] = .1048 or 10.48%

And the post-retirement APR is:

EAR = .08 = [1 + (APR/12)] 12 -1

APR = 12[(1.08) 1/12 -1] = .0772 or 7.72%

First, we will calculate how much he needs at retirement. The amount needed at retirement is the PV of the monthly spending plus the PV of the inheritance. The PV of these two cash flows is:

PVA = $24500{1 -[1/(1 + .0772/12) 12(25) ]}/(.0772/12) = $3,252,096.21

PV = $1525,000/[1 + (.0772/12)] 300 = $222,723.58

So, at retirement, he needs:

$3,252,096.21+ $222,723.58= $3474819.79

He will be saving $2,600 per month for the next 10 years until he purchases the cabin. The value of his savings after 10 years will be:

FVA = $2,600[{[1 + (.1048/12)] 12(10) -1}/(.1048/12)] = $547,487.10

After he purchases the cabin, the amount he will have left is:

$547,487.10 -345,000 = $202487.10

He still has 20 years until retirement. When he is ready to retire, this amount will have grown to:

FV = $202487.10[1 + (.1048/12)] 12(20) = $1632023.27

So, when he is ready to retire, based on his current savings, he will be short:

$3474819.79-1632023.27 = $1842796.52

This amount is the FV of the monthly savings he must make between years 10 and 30. So, finding the annuity payment using the FVA equation, we find his monthly savings will need to be:

FVA = $1842796.52 = C [{[ 1 + (.1048/12)] 12(20) -1}/(.1048/12)]

C = $2,279.60

He would have to save each month in years 11 through 30 the amount of $2,279.60