Math Problem Statement

On December 30, you make a $4,800 charitable donation.

If you are in the 24 percent tax bracket, how much will you save in taxes for the current year?

If you deposit that tax savings in a savings account for the next 5 years at 8 percent, what will be the future value of that account?

Note: Round FV factor to 3 decimal places and final answer to 2 decimal places.

Solution

Step 1: Calculate the tax savings

Since you are in the 24% tax bracket, you will save 24% of your charitable donation in taxes.

Tax savings=4,800×0.24=1,152\text{Tax savings} = 4,800 \times 0.24 = 1,152

So, the tax savings will be $1,152.

Step 2: Calculate the future value of the tax savings

The tax savings of $1,152 will be deposited into a savings account with an interest rate of 8% for 5 years. We will use the Future Value formula for compound interest:

FV=PV×(1+r)nFV = PV \times (1 + r)^n

Where:

  • FVFV is the future value,
  • PV=1,152PV = 1,152 is the present value (tax savings),
  • r=0.08r = 0.08 is the annual interest rate,
  • n=5n = 5 is the number of years.

Let's calculate this step by step:

FV=1,152×(1+0.08)5FV = 1,152 \times (1 + 0.08)^5

FV=1,152×(1.469)FV = 1,152 \times (1.469)

FV1,692.29FV \approx 1,692.29

Final Answer:

The future value of the account will be $1,692.29 after 5 years.


Would you like further details or have any questions?

Here are 5 related questions you might find interesting:

  1. How would the future value change if the interest rate were 10% instead of 8%?
  2. What if you deposited the tax savings for 10 years instead of 5?
  3. How is compound interest different from simple interest in this context?
  4. How does the tax bracket affect the tax savings in this scenario?
  5. What are the implications of making larger charitable donations in terms of tax savings?

Tip: When saving money, higher interest rates and longer durations result in significantly larger future values due to compound interest!

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Math Problem Analysis

Mathematical Concepts

Tax Calculation
Compound Interest
Percentage

Formulas

Tax savings = Donation Amount × Tax Bracket
Future Value (FV) = Present Value (PV) × (1 + r)^n

Theorems

Compound Interest Theorem

Suitable Grade Level

Grades 9-12