Morris has $1,000 to invest. He is considering two investment options.
Option A pays 0.5% simple interest.
Option B pays 0.75% interest compounded annually.
What is the value of each investment option at 5 years?
1000(1 + 0.005*5) = ____
1000(1 + 0.0075)^5 = ____
To find the value of each investment option at 5 years, we can use the formula for simple interest and compound interest.
For Option A, which pays 0.5% simple interest, the formula is:
Value = Principal + (Principal * Interest * Time)
Substituting the given values:
Principal = $1,000
Interest = 0.5% = 0.005
Time = 5 years
Value = $1,000 + ($1,000 * 0.005 * 5)
Value = $1,000 + ($1,000 * 0.025)
Value = $1,000 + $25
Value = $1,025
Therefore, Option A would have a value of $1,025 after 5 years.
For Option B, which pays 0.75% interest compounded annually, the formula is:
Value = Principal * (1 + Interest)^Time
Substituting the given values:
Principal = $1,000
Interest = 0.75% = 0.0075
Time = 5 years
Value = $1,000 * (1 + 0.0075)^5
Value ≈ $1,000 * 1.038
Value ≈ $1,038
Therefore, Option B would have a value of approximately $1,038 after 5 years.
To calculate the value of each investment option at 5 years, we need to use the given interest rates and formulas for simple interest and compound interest.
First, let's calculate the value of Option A using simple interest.
Option A pays 0.5% simple interest, which means that the interest earned each year is 0.5% of the principal amount (initial investment). The formula for calculating the value of an investment with simple interest is:
Value = Principal + (Principal * Rate * Time)
In this case, the Principal amount (initial investment) is $1,000 and the Rate is 0.5% (0.005 in decimal form). The Time is 5 years.
So, the value of Option A after 5 years can be calculated as follows:
Value of Option A = $1,000 + ($1,000 * 0.005 * 5)
= $1,000 + ($1,000 * 0.025)
= $1,000 + $25
= $1,025
Therefore, after 5 years, Option A will have a value of $1,025.
Now, let's calculate the value of Option B using compound interest.
Option B pays 0.75% interest compounded annually. This means that the interest is added to the investment at the end of each year, and in the subsequent years, the interest is calculated based on the new total value (including the interest).
The formula for calculating the value of an investment with compound interest is:
Value = Principal * (1 + Rate)^Time
In this case, the Principal amount (initial investment) is $1,000, the Rate is 0.75% (0.0075 in decimal form), and the Time is 5 years.
So, the value of Option B after 5 years can be calculated as follows:
Value of Option B = $1,000 * (1 + 0.0075)^5
Using a calculator or computer program, we can evaluate this expression. The approximate value of Option B after 5 years is $1,038.65 (rounded to the nearest cent).
Therefore, after 5 years, Option B will have a value of approximately $1,038.65.
In summary, the value of Option A at 5 years is $1,025, and the value of Option B is approximately $1,038.65.