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 goes beyond the Compound Interest Table. Calculate the new table factor for this investment.
Calculate the compound amount. Use the compound amount formula and a calculator. (Round your answer to two decimal places.)
P = $8100, r = 3% compounded monthly, t = 10 years
To calculate the compound amount using an interest rate of 6% compounded monthly after 4 years, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = Compound amount (final value)
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, the principal amount (P) is $10,000, the annual interest rate (r) is 6% (0.06 as a decimal), the interest is compounded monthly, so the number of times compounded per year (n) is 12, and the number of years (t) is 4.
Plugging in these values into the formula, we get:
A = 10000 * (1 + 0.06/12)^(12*4)
Now, to find the new table factor, we need to divide the compound amount (A) by the principal amount (P):
table factor = A / P
table factor = (10000 * (1 + 0.06/12)^(12*4)) / 10000
Simplifying the expression, we can cancel out the common terms:
table factor = (1 + 0.06/12)^(12*4)
Now, calculate the resulting value for the table factor using a calculator or a spreadsheet software. The table factor will give you the factor by which the principal amount is multiplied to calculate the compound amount.