Find the present value of the future value of $1,000,000 invested at 12% interest compounded monthly for 50 years.
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.
![**Present Value Calculation**
Given: Find the present value of a future value of $1,000,000 invested at 12% interest compounded monthly for 50 years.
To solve this problem, use the present value formula for compound interest:
\[ PV = \frac{FV}{(1 + \frac{r}{n})^{nt}} \]
Where:
- \( PV \) is the present value.
- \( FV \) is the future value ($1,000,000).
- \( r \) is the annual interest rate (12% or 0.12).
- \( n \) is the number of times the interest is compounded per year (12 for monthly).
- \( t \) is the time in years (50).
\[ PV = \frac{1,000,000}{(1 + \frac{0.12}{12})^{12 \times 50}} \]
\[ PV = \frac{1,000,000}{(1 + 0.01)^{600}} \]
Calculate the divisor:
\[ (1.01)^{600} \approx 29.96 \]
\[ PV = \frac{1,000,000}{29.96} \]
Finally:
\[ PV \approx 33,389.21 \]
The present value of $1,000,000 invested at 12% interest compounded monthly for 50 years is approximately $33,389.21.
(Note: The calculation of \((1.01)^{600}\) might vary slightly based on the precision of the calculator used.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F199c7314-0602-454d-8cb1-bd7542ff2956%2Fb8058cff-5aa2-4246-8ce8-00dc672d4da1%2Frogevz_processed.jpeg&w=3840&q=75)
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