In: Finance
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 $ 880 Second birthday 880 Third birthday 980 Fourth birthday 850 Fifth birthday 1,080 Sixth birthday 950 After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $380,000. If the relevant interest rate is 11 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.) Future value $
Future Value(FV) of Cash flow : | ||||||||||
Cash Flow*((1+i)^(T-n)) | ||||||||||
i=interest Rate | ||||||||||
T= Year end of Future Value | ||||||||||
n=Year of Cash Flow | ||||||||||
n | Year | 1 | 2 | 3 | 4 | 5 | 6 | |||
A | Cash Flow | $880 | $880 | $980 | $850 | $1,080 | $950 | |||
i | Interest Rate(11%) | 0.11 | 0.11 | 0.11 | 0.11 | 0.11 | 0.11 | |||
T | Year end of future value | 6 | 6 | 6 | 6 | 6 | 6 | SUM | ||
B=A*(1.11^(6-n)) | Future value of cash flow at end of year6 | $1,483 | $1,336 | $1,340 | $1,047 | $1,199 | $950 | $7,355 | ||
Value of deposits at end of 6 years | $7,355 | |||||||||
Number of years to age of 65 | 59 | (65-6) | ||||||||
Interest rate during the period(7%) | 0.07 | |||||||||
Value of deposit at age of 65 years | $398,320.30 | (7355*(1.07^59)) | ||||||||
Value of deposit at maturity of policy | $398,320.30 | |||||||||