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: |
$ |
910 |
| Second birthday: |
$ |
910 |
| Third birthday: |
$ |
1,010 |
| Fourth birthday: |
$ |
1,010 |
| Fifth birthday: |
$ |
1,110 |
| Sixth birthday: |
$ |
1,110 |
After the child's sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $420,000.
Required:
If the relevant interest rate is 11 percent for the first six years and 7 percent for all subsequent years, what is the value of the policy at the child's 65th birthday?