An insurance company is offering a new policy to its customers. Typically the po
ID: 2818689 • Letter: A
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 $ 850 Second birthday $ 850 Third birthday $ 950 Fourth birthday $ 850 Fifth birthday $ 1,050 Sixth birthday $ 950 After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $350,000. 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.)
Explanation / Answer
deposit on 1st birthday , d1 = $850
deposit on 2nd birthday , d2 = $850
deposit on 3rd birthday , d3 = $950
deposit on 4th birthday , d4 = $850
deposit on 5th birthday , d5 = $1050
deposit on 6th birthday , d6 = $950
interest rate for first 6 years , r1 = 10% = 0.10
interest rate after first 6 years , r2 = 7% = 0.07
value of deposits at the end of 6 years = v = [d1*(1+r1)5 ] +[d2*(1+r1)4 ] +[d3*(1+r1)3 ] +[d4*(1+r1)2 ] +[d5*(1+r1) ] + d6
= [850*(1.10)5 ] +[850*(1.10)4 ] +[950*(1.10)3 ] +[850*(1.10)2 ] +[1050*(1.10) ] + 950
= 1368.93350 + 1244.48500 + 1264.45000 +1028.50000 + 1155 + 950
= 7011.3685
value of deposits when policy matures = v + v*(1+r2)59 = 7011.3685 + [7011.3685*(1.07)59
= 7011.3685 + 379704.4409 = $386,715.80943 or $386,715.81 ( rounding off to 2 decimal places)
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