Solve the following problem by using the compound interest formula.
The FernRod Motorcycle Company invested $260,000 at 3.5% compounded monthly to be used for the expansion of their manufacturing facilities. How much money will be available for the project in years? Round the monthly rate in decimal form to four decimal places. Round your answer to the nearest dollar. Do not round any other intermediate calculations.
$ _________
how many years?
In any case, after t years, the amount will be
260000(1 + 0.035/12)^(12t)
so do the math
To solve this problem using the compound interest formula, we can use the following formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money available for the project
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this problem, the principal amount (P) is $260,000, the annual interest rate (r) is 3.5% (or 0.035 in decimal form), the interest is compounded monthly (n = 12), and we need to find the amount of money available after a certain number of years (t).
Let's substitute the values into the formula and solve for A:
A = 260,000(1 + 0.035/12)^(12t)
To find the amount of money available after a certain number of years, you need to know the value of 't'. Once you have that value, you can use a calculator to evaluate the expression and find 'A'.
Note: The problem states to round the monthly rate to four decimal places and round the final answer to the nearest dollar. Make sure to follow these rounding instructions when calculating the answer.