At age 25, Jesus deposited $2000 each year into an annuity. His annuity paid 8.5% interest. He continued depositing that amount until he retired at age 65. a)Find the future value of the account b)Find Jesus' total contributions to the account. c) Find the total interest earned.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
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Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![**Retirement Savings Problem**
At age 25, Jesus deposited $2000 each year into an annuity. His annuity paid 8.5% interest.
He continued depositing that amount until he retired at age 65.
**Problems:**
a) Find the future value of the account.
b) Find Jesus’ total contributions to the account.
c) Find the total interest earned.
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**Instructions for Solving the Problems:**
1. **Future Value of the Account:**
- Use the future value formula for an ordinary annuity:
\[
FV = PMT \times \frac{(1 + r)^n - 1}{r}
\]
where:
- \(FV\) is the future value of the annuity.
- \(PMT\) is the annual payment ($2000).
- \(r\) is the annual interest rate (8.5% or 0.085).
- \(n\) is the number of years the deposits are made (65 - 25 = 40 years).
2. **Total Contributions to the Account:**
- Calculate the total amount Jesus contributed by multiplying the annual deposit by the number of years:
\[
\text{Total Contributions} = PMT \times n
\]
3. **Total Interest Earned:**
- Subtract the total contributions from the future value of the account:
\[
\text{Total Interest Earned} = FV - \text{Total Contributions}
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