Use a calculator to evaluate an ordinary annuity formula
A = m
1 +
r
n
nt
− 1
r
n
for m, r, and t (respectively). Assume monthly payments. (Round your answer to the nearest cent.)
$100; 6%; 11 yr
sorry - your eye-watering text formatting makes me disinclined to figure out what you have written.
there are lots of handy online calculators you can use. A good one is wolframalpha.com
Just enter your expression. Be sure to use enough parentheses to ensure that it is interpreting your input correctly.
To evaluate the ordinary annuity formula with the given values, we will substitute the following values:
m = $100 (monthly payment)
r = 6% (annual interest rate)
t = 11 years
Step 1: Convert the annual interest rate to a monthly interest rate. Since we are assuming monthly payments, we need to divide the annual interest rate by 12.
Monthly interest rate = r / 12 = 6% / 12 = 0.06 / 12 = 0.005
Step 2: Calculate the total number of payments. Since the payments are made monthly for 11 years, we multiply the number of years by 12.
Number of payments = t * 12 = 11 * 12 = 132
Step 3: Substitute the values into the ordinary annuity formula and evaluate it using a calculator:
A = m * (1 + r / n)^(n * t) - 1) / (r / n)
A = $100 * (1 + 0.005)^132 - 1) / (0.005)
Calculating the expression inside the brackets first:
(1 + 0.005)^132 = 1.005^132 = 1.34009624
Now substitute this value into the annuity formula:
A = $100 * (1.34009624 - 1) / 0.005
Calculating the numerator:
$100 * (1.34009624 - 1) = $34.009624
Now calculate the final answer:
A = $34.009624 / 0.005
A = $6,801.92 (rounded to the nearest cent)
Therefore, the value of the ordinary annuity formula with the given values is approximately $6,801.92.
To evaluate the ordinary annuity formula using a calculator, you will need to substitute the given values of m, r, and t into the formula. Here's how you can do it step by step:
1. Start by dividing the annual interest rate (r) by the number of compounding periods per year (n). In this case, since it's assumed to have monthly payments, the number of compounding periods per year is 12. So, we have:
r/n = 6% / 12 = 0.06 / 12 = 0.005
2. Multiply the number of compounding periods by the number of years to get the total number of periods (nt). In this case:
nt = 12 * 11 = 132
3. Plug these values into the annuity formula:
A = m * (1 + r/n)^(nt) - 1 / (r/n)
Now, substitute the given values:
m = $100
r/n = 0.005
nt = 132
A = $100 * (1 + 0.005)^(132) - 1 / (0.005)
Before proceeding further, it is important to clarify the order of operations. When using a calculator, you need to be careful with the sequence of calculations. Many calculators use the BEDMAS order of operations:
B - Brackets
E - Exponents (Powers and roots)
D - Division
M - Multiplication
A - Addition
S - Subtraction
So, to correctly enter the expression into a calculator, you must follow the BEDMAS order of operations.
4. Now, enter the expression into your calculator, following the proper order of operations.
$100 * (1 + 0.005)^132 - 1 / 0.005
Important: Remember to use parentheses to group the numerator and denominator of the last fraction, so it's clear to the calculator what needs to be divided.
5. Evaluate the expression on your calculator and round the final answer to the nearest cent.
The calculator should give you the value of the ordinary annuity (A) rounded to the nearest cent.