A bank is offering a special three year investment certificate paying 3.25% per year, compounded monthly. How much interest would you earn by the end of the three years if you deposited $1500 in the account?
To calculate the interest earned at the end of three years on a special three-year investment certificate that pays 3.25% per year, compounded monthly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount including interest
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, the principal amount (P) is $1500, the interest rate (r) is 3.25% per year (or 0.0325 as a decimal), the compounding frequency (n) is monthly (or 12 times per year), and the investment period (t) is three years.
Plugging in these values, we can calculate the final amount (A):
A = 1500(1 + (0.0325/12))^(12*3)
Let's break down this calculation step by step:
Step 1: Calculate the monthly interest rate:
monthly interest rate = annual interest rate / number of compounding periods per year
monthly interest rate = 0.0325 / 12 = 0.0027083333
Step 2: Calculate the total number of compounding periods:
total number of compounding periods = number of compounding periods per year * number of years
total number of compounding periods = 12 * 3 = 36
Step 3: Calculate the final amount:
A = 1500(1 + 0.0027083333)^(36)
Now, you can use a calculator or a spreadsheet to raise the expression (1 + 0.0027083333) to the power of 36, and then multiply it by $1500 to find the final amount (A).
Once you have the final amount (A), you can subtract the principal amount ($1500) to calculate the total interest earned over the three-year period.