Question

In: Finance

An insurance company is offering a new policy to its customers. Typically, the policy is bought...

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          

Solutions

Expert Solution

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

Expert Solution

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


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