Suppose you deposit $900 at the end of every 6 months in an account that pays 4.5% interest compounded semi-annually for 7 years. What is the value of the annuity at the end of 7 years? a) $13,417 b) $14,619 c) $26,045 d) $54,619 e) None of these
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
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
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.
![### Financial Mathematics Problem
#### Trigonometric Expression
Given:
\[ y = 3 \sin 60^\circ = 3 \cdot \frac{\sqrt{3}}{2} = \frac{3\sqrt{3}}{2} \]
#### Annuity Calculation Problem
Suppose you deposit $900 at the end of every 6 months in an account that pays 4.5% interest compounded semi-annually for 7 years. What is the value of the annuity at the end of 7 years?
##### Options:
a) $13,417
b) $14,619
c) $26,045
d) $54,619
e) None of these
#### Note
To solve the annuity calculation problem, the formula for the future value of an ordinary annuity compounded semi-annually can be used:
\[ FV = P \left( \frac{(1 + r/n)^{nt} - 1}{r/n} \right) \]
Where:
- \( FV \) is the future value of the annuity.
- \( P \) is the payment amount ($900).
- \( r \) is the annual interest rate (4.5% or 0.045).
- \( n \) is the number of times interest is compounded per year (2 for semi-annually).
- \( t \) is the number of years (7).
By substituting the values:
\[ FV = 900 \left( \frac{(1 + 0.045/2)^{2 \cdot 7} - 1}{0.045/2} \right) \]
Calculating this will give the value of the annuity at the end of 7 years.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9abca75-4ac1-4aa6-8dd1-abe767689103%2Fe14d9342-315c-4b28-ba8b-ffd5042b6b79%2F13q6oqk_reoriented.jpeg&w=3840&q=75)
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