A new father plans on saving for his daughter’s college education. He will donate $775.00 on her first birthday. After that, he will increase his donation by 6.00% each year and will make his last contribution on her 18th birthday. If he can earn 10.00% each year in his investment account, how much will his daughter’s college fund be worth on her 18th birthday?



To solve this problem, we need to consider the yearly donations, the annual increase in the amount donated, and the 10% annual interest rate in the investment account. Here's a step-by-step breakdown of how we can calculate the future value of the college fund.

### Step 1: Identifying the parameters
- Initial donation ($D_1$) = $775.00
- Annual increase = 6%
- Interest rate ($r$) = 10%
- The father will donate every year for 18 years (from the 1st birthday to the 18th).

The donations follow a **geometrically increasing sequence** because each donation increases by 6% every year. We need to calculate the **future value** (FV) of each donation, considering that each donation earns 10% interest until her 18th birthday.

### Step 2: Calculate the future value of each contribution
The future value of an investment growing with a constant interest rate is given by:

\[
FV = P \times (1 + r)^{n}
\]

Where:
- $P$ is the principal amount (the donation in each year),
- $r$ is the interest rate (10% or 0.10),
- $n$ is the number of years the investment grows.

Since the father makes donations from the 1st birthday to the 18th birthday, each donation will have a different number of years to grow. The donation on the 1st birthday will grow for 17 years, the donation on the 2nd birthday will grow for 16 years, and so on, until the last donation on the 18th birthday, which will grow for 0 years.

### Step 3: Total future value of the contributions
Each year, the donation grows by 6%. So, we need to sum up the future values of all the donations from year 1 to year 18. Let's calculate this using the formula for the future value of increasing payments in a geometric progression. I'll compute this next.

The total value of the daughter's college fund on her 18th birthday will be approximately **$52,420.58**.

Would you like further details on any part of the calculation? Here are some related questions to deepen understanding:

1. How would the future value change if the interest rate were 8% instead of 10%?
2. What if the father increased his contributions by 5% instead of 6% each year?
3. How much would the college fund be if no interest were earned at all?
4. How many years would it take to reach $100,000 at the current savings and interest rate?
5. What if the father skipped a few years of contributions — how would that affect the final value?

**Tip:** The earlier you invest in a fund that compounds interest, the more growth you'll see due to the power of compound interest.

A new father plans on saving for his daughter’s college education. He will donate $775.00 on her first birthday. After that, he will increase his donation by 6.00% each year and will make his last contribution on her 18th birthday. If he can earn 10.00% each year in his investment account, how much will his daughter’s college fund be worth on her 18th birthday?

Learn how to calculate the future value of a college fund with yearly contributions increasing by 6% and earning 10% annual interest. This problem covers compound interest and geometric progression, suitable for high school students and financial planning enthusiasts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation