Question

Jerber Corp. is offering a novel retirement plan. The plan targets grandparents who often give their grandchildren large amounts of money until the children reach school age. The buyer of the retirement plan (say, a grandparent) makes six annual payments to Jerber Corp. on each of the first six birthday's of a grandchild.

First birthday:$760   

Second birthday:$760   

Third birthday:$860   

Fourth birthday:$850   

Fifth birthday:$960   

Sixth birthday:$950

No more payments are made to Jerber Corp. after the child’s sixth birthday. When the grandchild reaches the age of 65, he or she is promised to receive $260,000. If the relevant interest rate on this type of investment is 10 percent for the first six years, and 7 percent for all subsequent years.

Compute the future value of the payments on the granchild's 65^th birthday. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Future Value= ?????

Answer 1

CF1 or first birthday Deposit = 760

CF 2= 760

CF3= 860

CF4= 850

CF5= 960

CF6= 950

Interest rate (I)= 10%

Year of last deposit (n)= 6

FV of all cash flows (at year 6) = CF1*(1+I)^(n-1) + CF2(1+I)^(n-2) + CF3*(1+I)^(n-3) + CF4*(1+I)^(n-4) +CF5*(1+I)^(n-5) +CF6*(1+I)^(n-6)

=(760*(1+10%)^(6-1)) + (760*(1+10%)^(6-2)) + (860*(1+10%)^(6-3)) + (850*(1+10%)^(6-4)) +(960*(1+10%)^(6-5)) +(950*(1+10%)^(6-6))

=6515.8636

Value at year 6 or PV = 6515.8636

Number of years from 6 to 65 (n)= 59

Interest rate (I)= 7%

FV (as on 65th year)= PV *(1+I)^n

=6515.8636*(1+7%)^59

=352870.1059

So future value is $352870.11