At the time of her grandson's birth, a grandmother deposits $2000 in an account that pays 8.5% compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period? The value of the account will be $. (Round to the nearest dollar as needed.)
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.
![**Compound Interest Calculation Example**
**Scenario:**
At the time of her grandson's birth, a grandmother deposits $2000 in an account that pays 8.5% compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period?
**Calculation:**
The value of the account will be $____.
(Round to the nearest dollar as needed.)
**Discussion:**
This exercise is an application of compound interest, where interest earned is added to the principal, so that the interest of the subsequent period is computed over the principal plus previously accrued interest. In this case, the interest is compounded monthly, which means it is calculated 12 times a year.
To learn how to solve this, use the compound interest formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount ($2000).
- \( r \) is the annual interest rate (8.5% or 0.085).
- \( n \) is the number of times that interest is compounded per year (12 for monthly).
- \( t \) is the time the money is invested for in years (21 years).
The required calculation involves substituting these values into the formula, which will yield the final account balance at the grandson's 21st birthday.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58fa9ca8-a7e7-4ecd-98e6-0e2121b1f6b9%2F3e9f910f-cd6c-488d-8dd7-3ad40e4ef475%2Fgi5d9y2_processed.jpeg&w=3840&q=75)
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