Calculating the Required APR

Oct 13, 2025 by wbrum.org 125 views

Introduction

As a new parent, Jason and Piera are eager to start saving for their newborn son, Joseph's, future education expenses. They have set a goal to have $40,000 available for him when he turns 18. To achieve this goal, they plan to deposit $100 into a college savings account each month. In this article, we will calculate the required APR (Annual Percentage Rate) for their college savings account to reach their goal.

Understanding the Problem

To calculate the required APR, we need to consider the following factors:

The total amount needed for Joseph's education expenses: $40,000
The monthly deposit amount: $100
The number of months until Joseph turns 18: 18 years * 12 months/year = 216 months

Calculating the Required APR

To calculate the required APR, we can use the formula for compound interest:

A = P x (1 + r/n)^(n*t)

Where:

A = the future value of the investment/loan, including interest ($40,000)
P = the principal investment amount (the initial deposit)
r = the annual interest rate (APR)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for

Since Jason and Piera plan to deposit $100 each month, we can use the formula for compound interest with monthly compounding:

A = P x (1 + r/12)^(12*t)

We want to find the required APR (r) to reach a future value of $40,000 after 216 months.

Solving for the Required APR

Rearranging the formula to solve for r, we get:

r = (A/P)^(1/(n*t)) - 1

Plugging in the values, we get:

r = ($40,000 / $100)^(1/(12*216)) - 1

r ≈ 0.0625 or 6.25%

Conclusion

To reach their goal of having $40,000 available for Joseph's education expenses when he turns 18, Jason and Piera need to earn an APR of approximately 6.25% on their college savings account. This means that their account must earn interest at a rate of 6.25% per year, compounded monthly.

Implications for Jason and Piera

To achieve their goal, Jason and Piera can consider the following options:

High-yield savings accounts: They can open a high-yield savings account with a bank or credit union that offers a competitive APR.
Certificates of deposit (CDs): They can invest in CDs with a term length that matches their time horizon (18 years).
Mutual funds or exchange-traded funds (ETFs): They can invest in a diversified portfolio of stocks or bonds through a mutual fund or ETF.
529 college savings plans: They can consider opening a 529 college savings plan, which offers tax benefits and flexibility.

Recommendations

Based on our calculation, Jason and Piera should aim to earn an APR of at least 6.25% on their college savings account. They can consider the options mentioned above and consult with a financial advisor to determine the best course of action for their specific situation.

Future Research Directions

This article has focused on calculating the required APR for a college savings account. Future research directions could include:

Investigating the impact of inflation on college savings goals
Analyzing the effects of different investment strategies on college savings outcomes
Examining the role of tax benefits in college savings plans

By understanding the required APR for their college savings account, Jason and Piera can make informed decisions about their investment strategy and work towards their goal of saving $40,000 for Joseph's education expenses.