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. For this policy, the purchaser, say, the parent, makes the following six payments to the insurance company:

First birthday $ 820

Second birthday $ 820

Third birthday $ 920

Fourth birthday $ 850

Fifth birthday $ 1,020

Sixth birthday $ 950

After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $320,000. If the relevant interest rate is 10 percent for the first six years and 7 percent for all subsequent years, what would the value of the deposits be when the policy matures? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Year	cash flow	future value of cash = cash flow*(1+r)^n-1, n-2……….n-n n = 6 r = 10%
1	820	1320.6182
2	820	1200.562
3	920	1224.52
4	850	1028.5
5	1020	1122
6	950	950
future value of annual savings at the end of year 6	sum of future value of annual cash flow	6846.2002
future value of sum of future value at the end of age 65	sum of future value at end of year 6*(1+r)^n	6846.20*1.07^59	370759.65
value of deposits			370759.65