How to determine the compound amount of an investment of $10,000 with an interest rate of 6%compounded monthly after 4 years requires you to use a table factor that beyond the compound Interest table. In how do you calculate the new table factor for this investment.
To calculate the compound amount of an investment using compound interest, you can use the formula:
A = P(1 + r/n)^(nt)
Where:
A is the compound amount (final value)
P is the principal amount (initial investment)
r is the interest rate (as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In your case, the principal (P) is $10,000, the interest rate (r) is 6% or 0.06, and it is compounded monthly, so n is 12. The investment period is 4 years (t).
The formula becomes:
A = 10000(1 + 0.06/12)^(12*4)
To evaluate this expression or calculate the compound amount, you can use a scientific calculator or a spreadsheet software like Excel.
However, you mentioned using a table factor. Typically, a compound interest table consists of pre-calculated values for different combinations of interest rates, compounding periods, and time periods. If you have a table that includes the interest rate of 6% compounded monthly for different time periods, you can find the corresponding table factor for 4 years and use it to calculate the compound amount.
If you don't have a pre-calculated table or want to calculate a new table factor for this specific investment, you can follow these steps:
1. Divide the interest rate by the number of compounding periods per year:
0.06/12 = 0.005
2. Multiply the number of compounding periods per year by the number of years:
12 * 4 = 48
3. Calculate the new table factor using the expression:
(1 + 0.005)^48
This will give you the new table factor for this investment, which you can then multiply by the principal amount ($10,000) to find the compound amount.