How Much Bob And Carol Need To Save For Their Baby's Birth
How much Bob and Carol need to save for their baby's birth costs in four years
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 $6,500 after all insurance payments. Pre-natal care costs amount to $2,000 out-of-pocket for the 12 months prior to the birth. Additionally, they plan to purchase a crib, a baby carrier, and other miscellaneous items costing $1,200 today, which will increase in cost by 10% annually over the next four years due to inflation. Uncle Ted has promised to contribute $1,000 at the end of year two for baby expenses. Bob and Carol currently have $500 to deposit in the bank, which earns 6% annually compounded interest.
The tasks are to (1) draw a timeline illustrating the timing of all relevant events, (2) calculate the total amount Bob and Carol will need in the bank on the day the baby is born to cover all expenses, and (3) determine how much they need to save at the end of each year to reach their goal.
Paper For Above instruction
Introduction
Planning for the financial demands of a new child involves meticulous estimation and strategic saving. For Bob and Carol, understanding the timing of expenses and how inflation and interest rates impact savings is crucial. This paper provides a comprehensive analysis of their projected expenses, the timeline of events, and the savings strategy necessary to meet their goal of having sufficient funds at the time of their child’s birth in four years.
Timeline of Events
The timeline of expenses and contributions can be summarized as follows:
- Present (Year 0): Bob and Carol have $500 to deposit, and expenses for baby items ($1,200) paid on the day of birth. They also plan to start saving at this point.
- Year 1 (12 months before birth): Pre-natal care costs of $2,000 are incurred.
- Year 2: Uncle Ted contributes $1,000 at the end of this year for baby expenses; they will continue saving.
- Year 3: No specific expense scheduled, but inflation on baby items increases costs by 10%.
- Year 4 (Year of birth): The primary expenses to be paid are the hospital costs of $6,500, plus the inflated cost of baby items purchased at that time. All savings accumulated up to this point will be used to cover these costs.
Calculating Future Costs of Baby Items
The baby items cost $1,200 today; increasing by 10% annually, their cost at the time of birth will be calculated using compound inflation:
\[
\text{Future Cost} = 1200 \times (1 + 0.10)^4 = 1200 \times 1.4641 = \$1,756.92
\]
Total Medical and Pre-natal Expenses
Pre-natal costs of $2,000 are paid in Year 1, and hospital costs of $6,500 are paid in Year 4, at the time of birth.
Total Expenses at Birth
Adding all these costs:
- Hospital costs: $6,500
- Inflated baby items: $1,756.92
Total expenses to be covered at Year 4 are:
\[
\$6,500 + \$1,756.92 = \$8,256.92
\]
Adjustments for Uncle Ted’s Contribution
Uncle Ted's $1,000 gift will be received at the end of Year 2 and can be used toward expenses or added to savings.
Present Value of Expenses and Savings
The calculation involves determining how much money is needed at Year 4 to pay for all expenses, accounting for interest earned on savings and timing of contributions. The current savings of $500 will grow over four years at 6%, and additional annual savings are necessary to meet the future cost.
Calculating Future Value of Current Savings and Required Annual Savings
Using the future value formula for a lump sum:
\[
FV = PV \times (1 + r)^n
\]
where PV = $500, r = 6%, n = 4, we get:
\[
FV_{current} = 500 \times (1 + 0.06)^4 = 500 \times 1.2625 = \$631.25
\]
To find the total amount needed at Year 4, subtract Uncle Ted’s contribution and the future value of current savings to determine the remaining amount to be accumulated through yearly savings.
Total future needs = $8,256.92 – $1,000 (Ted’s contribution) = $7,256.92
Remaining amount needed after current savings grow: $7,256.92 – $631.25 = $6,625.67
Now, to determine the annual savings (A) required over 4 years, assuming they save at the end of each year and earn 6%, we use the future value of an ordinary annuity formula:
\[
FV_{annuity} = A \times \frac{(1 + r)^n - 1}{r}
\]
solving for A:
\[
A = \frac{FV_{annuity}}{\frac{(1 + r)^n - 1}{r}} = \frac{6,625.67}{\frac{(1+0.06)^4 - 1}{0.06}} = \frac{6,625.67}{\frac{1.2625 - 1}{0.06}} = \frac{6,625.67}{4.375} \approx \$1,515.25
\]
Thus, Bob and Carol need to save approximately $1,515.25 at the end of each year over the next four years.
Conclusion
Effective financial planning requires meticulous calculation of expected costs and income streams, aligned with inflation and interest rates. For Bob and Carol, saving approximately $1,515 annually, combined with their initial deposit and Uncle Ted’s contribution, will enable them to cover all projected expenses when their child is born in four years. Through disciplined savings and understanding of the timing and growth of investments, they can ensure financial readiness for their new arrival.
References
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- Gitman, L. J., & Zutter, C. J. (2019). Principles of Managerial Finance (15th ed.). Pearson.
- Higgins, R. C. (2018). Analysis for Financial Management. McGraw-Hill Education.
- Ross, S. A., Westerfield, R. W., & Jaffe, J. (2019). Corporate Finance (12th ed.). McGraw-Hill Education.
- Investopedia. (2020). Future Value (FV). Retrieved from https://www.investopedia.com/terms/f/futurevalue.asp
- Bank of America. (2022). How to Plan for Your Child’s Future. Retrieved from https://www.bankofamerica.com/financial-center/financial-education/childrens-education-funding/
- U.S. Department of Health & Human Services. (2021). Guide to Prenatal Care Costs. Retrieved from https://www.hhs.gov
- Federal Reserve Bank. (2023). The Effects of Inflation on Savings. Retrieved from https://www.federalreserve.gov
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- American Academy of Pediatrics. (2020). Childbirth Costs and Financial Planning. Retrieved from https://www.aap.org