13 10 00 poines purchaser say the parent makes the tollowing

13. 10 00 poines purchaser (say, the parent) makes the tollowing six payments to the insurance company S 910 S 1,010 S 1,010 s 1,110 S 1,110 Third birthday Fifth birthday After the child\'s sath birthday, no more payments are made. When the child reaches age 65, he or she receives $420,000 If the relevant interest rate is 11 percent for the first six years and 7 percent for all subsequent years, what is the value of the policy at the chs 65th birthday? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g. 32.16.)

Solution

First we need calculate the value of premiums at 6th year

=910*(1.11)^5+910*(1.11)^4+1010*(1.11)^3+1010*(1.11)^2+1110*1.11+1110

=$7882.675

Now Future value at child\'s 65th birthday

=$7882.675*(1.07)^59

=$426890.50

Value= -$426890.50+ $420000= -$6890.53

The policy is not worth taking as Value of premium paid is higher than value of benefit recieved