QuestionSuppose that is loaned at a rate of , compounded monthly. Assuming that no payments are made, find the amount owed after 3 years. Do not round any intermediate computations, and round your answer to the nearest cent.
Studdy Solution
STEP 1
1. The principal amount is $2000.
2. The annual interest rate is 10.5%.
3. Interest is compounded monthly.
4. The loan period is 3 years.
5. No payments are made during this period.
6. We need to round the final answer to the nearest cent.
STEP 2
1. Identify the compound interest formula.
2. Determine the values for each variable in the formula.
3. Plug the values into the formula.
4. Calculate the result.
5. Round the answer to the nearest cent.
STEP 3
The compound interest formula is:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal balance
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
STEP 4
Let's determine the values for each variable:
P = $2000 (principal balance)
r = 0.105 (10.5% expressed as a decimal)
n = 12 (compounded monthly, so 12 times per year)
t = 3 (3 years)
STEP 5
Now, let's plug these values into our formula:
A = 2000(1 + 0.105/12)^(12*3)
STEP 6
Let's calculate this step by step:
1) First, calculate 0.105/12 = 0.00875
2) Add 1 to this: 1 + 0.00875 = 1.00875
3) Calculate the exponent: 12 * 3 = 36
4) Now we have: A = 2000(1.00875)^36
5) Calculate (1.00875)^36 ≈ 1.369648505
6) Multiply: 2000 * 1.369648505 ≈ 2739.297010
STEP 7
Rounding to the nearest cent:
2739.297010 rounds to $2739.30
Therefore, the amount owed after 3 years is $2739.30.
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