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 $ 800 Second birthday $ 800 Third birthday $ 900 Fourth birthday $ 850 Fifth birthday $ 1,000 Sixth birthday $ 950 After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $300,000. 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

Here,

CF₁ = $800

CF₂ = $800

CF₃ = $900

CF₄ = $850

CF₅ = $1,000

CF₆ = $950

From year 1 to Year 6,

Interest Rate = 10%

So,

Calculating Future Value at the end of Year 6,

Future Value = $6736.09

Policy will mature when Age = 65,

Calculating Future Value,

Time Period = 59 Years

Interest Rate = 7%

FV = PV(1 + r)^t

Future Value = 6736.09(1 + 0.07)⁵⁹

Future Value = $364,796.59

So,

Value of Policy at Year 65 = $364,796.59