Question

An insurance company is offering a new policy to its customers. Typically, the policy is bought by a parent or grandparent for a child at the child’s birth. The details of the policy are as follows: The purchaser (say, the parent) makes the following six payments to the insurance company:

First birthday:	$	780
Second birthday:	$	780
Third birthday:	$	880
Fourth birthday:	$	880
Fifth birthday:	$	980
Sixth birthday:	$	980

After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $210,000.

If the relevant interest rate is 12 percent for the first six years and 6 percent for all subsequent years, what is the value of the policy at the child's 65th birthday? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Child's 65th birthday          

Answer 1

Year	Payment	Future value of payment = annual payment*(1+r)^n-1	Future value of payment = annual payment*(1+r)^n-1
1	780	780*1.12^5	1374.626513
2	780	780*1.12^4	1227.345101
3	880	880*1.12^3	1236.33664
4	880	880*1.12^2	1103.872
5	980	980*1.12^1	1097.6
6	980	980*1.12^0	980
Future value of payment at the 6th birthday	sum of future value of payment		7019.780254
Future value of payment at 65th Birthday	value of payment at 6th birthday*(1+r)^n	7019.7802*1.06^59	218458.81

Answer 2

Amount	Formula used for compounding	Compounded amount
780	780*1.12^6*1.06^59	47,912.50
780	780*1.12^5*1.06^59	42,779.01
880	880*1.12^4*1.06^59	43,092.41
880	880*1.12^3*1.06^59	38,475.37
980	980*1.12^2*1.06^59	38,256.76
980	980*1.12^1*1.06^59	34,157.82
	Sum	2,44,673.87

Value at the end of 65 years = $244,673.87