Jerber Corp. is offering a novel retirement plan. The plan targets grandparents who often give their grandchildren large amounts of money until the children reach school age. The buyer of the retirement plan (say, a grandparent) makes six annual payments to Jerber Corp. on each of the first six birthday's of a grandchild. First birthday: $ 790 Second birthday: $ 790 Third birthday: $ 890 Fourth birthday: $ 850 Fifth birthday: $ 990 Sixth birthday: $ 950 No more payments are made to Jerber Corp. after the child’s sixth birthday. When the grandchild reaches the age of 65, he or she is promised to receive $290,000. If the relevant interest rate on this type of investment is 10 percent for the first six years, and 7 percent for all subsequent years.
Compute the future value of the payments on the granchild's 65th birthday.
future value = present value * (1 + rate)number of years
First, we compute the value of the payments on the child's 6th birthday.
Value of the payments on the child's 6th birthday = ($790 * (1 + 10%)5) + ($790 * (1 + 10%)4) + ($890 * (1 + 10%)3) + ($850 * (1 + 10%)2) + ($990 * (1 + 10%)1) + ($950 * (1 + 10%)0)
Value of the payments on the child's 6th birthday = $6,681.03
Next, we calculate the future value of this amount on the child's
65th birthday (which is 59 years after 6th birthday)
Future value = $6,681.03 * (1 + 7%)59 = $361,814.88
future value of the payments on the grandchild's 65th birthday = $361,814.88
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