Posted: March 4th, 2023
Bob and Carol are planning for the birth of their first child exactly four years from today. They are now ready to start their savings plan for the big event. The current hospital cost for having a healthy baby at the local hospital is $6500 after all insurance payments. Pre-natal care for the immediate 12-month period prior to having the baby amounts to $2000 in out-of-pocket costs. Carol’s best friend is planning a baby shower, so only a crib, a baby carrier, and other miscellaneous items will be needed, which all cost $1,200 today. However, these items will be purchased and paid for on the day of the child’s birth, and the items are expected to increase in costs by 10% each year over the next four years due to inflation.
Bob and Carol now have $500 in cash that they plan to put in the bank in order to cover all the new costs. Also, Uncle Ted has promised to contribute $1000 at the end of year two, as a present to Bob and Carol for baby expenses.
Currently, Bob and Carol can earn 6% compounded annually on this money. In order to be able to pay cash for all these expenses on the day the baby is born, how much will Bob and Carol have to save, assuming the baby is born exactly four years from today
SOLUTION
Therefore, the future value of Uncle Ted’s gift is $1,191.02.
Now we can add up the future values of all the costs to get the total amount that Bob and Carol need to save:
Total future value = $6,500 + $2,000 + $1,757.92 + $1,191.02 = $11,448.94
Therefore, Bob and Carol need to save $11,448.94 over the next four years to cover all the baby-related expenses. If they put their current $500 into a savings account that earns 6% compounded annually, and make regular contributions of $2,487.73 (calculated using the present value of an annuity formula), they will have exactly $11,448.94 at the end of four years.
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