Use a calculator to evaluate an ordinary annuity formula
A = m[(1+r/n)^nt -1 / (r/n)]
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
side note it is not not minus one it is (1+r/n)^nt minus 1
Rude. But you're right. Just type it in.
To evaluate the ordinary annuity formula, we'll substitute the given values for m, r, and t.
m = $100
r = 6% = 0.06 (decimal form)
n = 12 (monthly payments per year)
t = 11 years
Using these values in the formula:
A = m[(1+r/n)^nt - 1 / (r/n) + 1]
A = $100[(1+0.06/12)^(12*11) - 1 / (0.06/12) + 1]
Now we can calculate each part of the formula step-by-step:
Step 1: Calculate (1+r/n)^(nt)
(1+0.06/12)^(12*11) ≈ 1.4185
Step 2: Calculate (r/n)
0.06/12 = 0.005 (decimal form)
Step 3: Calculate [(1+r/n)^nt - 1 / (r/n)]
(1.4185 - 1) / 0.005 ≈ 283.7
Step 4: Calculate [m * ((1+r/n)^nt - 1) / (r/n) + 1]
$100 * 283.7 + 1 ≈ $28,370.00
Therefore, the value of the ordinary annuity formula with the given inputs is approximately $28,370.00.
To evaluate the ordinary annuity formula using a calculator, follow these steps:
1. Convert the interest rate from a percentage to a decimal. In this case, the interest rate is 6%, so divide it by 100: 6/100 = 0.06.
2. Calculate the number of compounding periods per year. Since the payments are monthly, the number of compounding periods per year is 12.
3. Calculate the total number of compounding periods (nt). In this case, the time period is 11 years, so multiply it by the number of compounding periods per year: 11 * 12 = 132.
4. Plug the given values into the annuity formula:
A = m * [(1 + r/n)^(nt) - 1 / (r/n)]
where:
m = Monthly payment amount = $100
r = Interest rate per compounding period = 0.06 (6% converted to decimal)
n = Number of compounding periods per year = 12
t = Total number of compounding periods = 132
A = 100 * [(1 + 0.06/12)^(12*11) - 1 / (0.06/12)]
5. Simplify the formula within the brackets:
[(1 + 0.005)^(132) - 1] / (0.005)
6. Use a calculator to calculate the value within the brackets:
(1 + 0.005)^(132) - 1
7. Calculate the final answer by dividing the result obtained in step 6 by 0.005:
Final Answer = [(Result of step 6) / 0.005]
After performing these calculations, you should have the evaluated value of the ordinary annuity formula.
you don't learn too well, do you?
Just type it in, so it makes sense, and is syntactically correct.
use google or wolframalpha.com and just enter
100[(1+.06/12)^(12*11) -1] / (.06/12)