the fernrod motorcycle company invested 250,000 at 4.5% compounded monthly to be used for the expansion of their manufacturing facilities. how much money will be aviable for the project 3.5 years?
Future value, F
Interest, i = 0.045
compounding frequency, f = 12
Time, t = 3.5 years
Let
P = present value, = 250000
then use the compound interest formula
F=P(1+i/f)ft
CGI
292,559
To calculate the amount of money available for the project after 3.5 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
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
Let's plug in the given values:
P = $250,000
r = 4.5% = 0.045 (since the rate is given in percentages, we divide it by 100 to convert it to a decimal)
n = 12 (compounded monthly, so 12 times per year)
t = 3.5 years
Using the formula:
A = 250,000 * (1 + 0.045/12)^(12 * 3.5)
Now let's calculate the answer step by step:
Step 1: Divide the annual interest rate (0.045) by the number of compounding periods per year (12):
0.045 / 12 = 0.00375
Step 2: Multiply the number of compounding periods per year (12) by the number of years (3.5):
12 * 3.5 = 42
Step 3: Add 1 to the result from Step 1:
1 + 0.00375 = 1.00375
Step 4: Raise the result from Step 3 to the power of the result from Step 2:
(1.00375)^(42) ≈ 1.187166
Step 5: Multiply the result from Step 4 by the principal amount:
250,000 * 1.187166 ≈ $296,791.50
Therefore, approximately $296,791.50 will be available for the expansion of their manufacturing facilities after 3.5 years.