Question

Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with retirement income of $30,000 per month for 15 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 15 years at an estimated cost of $675,000. Third, after he passes on at the end of the 15 years of withdrawals, he would like to leave an inheritance of $800,000 to his nephew Frodo. He can afford to save $2,300 per month for the next 15 years.

  

Required:

If he can earn a 9 percent EAR before he retires and a 7 percent EAR after he retires, how much will he have to save each month in years 16 through 30?

Answer 1

Since question has given EAR, and payment is given in monthly terms, so first we need to find out APR from the given EAR that is

For 7% EAR, APR is ((1.07)^(1/12) – 1)x12 = 6.784974

For 9% EAR, APR is ((1.09)^(1/12) – 1)x12 = 8.648788%

As per the given information, $30,000 per month is withdrawn for 15 years that is 180 months and a inheritance to be left for $800,000

The present value of the above sums when she retires will be as follows:

Set the following in financial calculator

N = 180, PMT = 30,000, I/Y = 6.784974/12, FV = 800,000

Press CPT + PV result would be 3672717.39

• Value of 2300 deposited each month for 15 years will be

N = 180, PMT = 2300, I/Y = 8.648788/12

Press CPT + FV , result would be 843,268.63, out of which 675,000 would be used towards purchasing a cabin, so balance remaining is 168,268.63

Its accumulated value at retirement would be

PV = 168268.63, N = 180, I/Y = 8.648788/12

Press CPT + FV result would be 612,915.53

Now we need remaining fund balance by depositing in 16 to 30 years that is (3672717.39-612915.53) = 3059801.86

Now set FV = 3059801.86, N = 180, I/Y = 8.648788/12

Press CPT + PMT result would be $8,345.55

So Bilbo needs to deposit $8,345.55 each month from year 16 to 30