If $200 is borrowed with an interest of 18.0% compounded monthly, what is the total amount of money needed to pay it back in 1 year? Round your answer to the nearest cent. Do not round at any other point in the solving process; only round your answer.
Answer (2)
The total amount of money needed to repay a $200 loan at an 18.0% interest rate compounded monthly after 1 year is approximately $239.12. This is calculated using the compound interest formula. After performing the necessary calculations and rounding, we find the final amount owed.
;
To find the total amount of money needed to pay back a loan with interest compounded monthly, we use the compound interest formula:
A = P ( 1 + n r ) n t
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount 20 .
r is the annual interest rate (decimal) 0.18 .
n is the number of times that interest is compounded per year (12 for monthly).
t is the time the money is invested or borrowed for, in years (1 year).
Plugging in the values:
P = 200
r = 0.18
n = 12
t = 1
The formula becomes:
A = 200 ( 1 + 12 0.18 ) 12 × 1
We first calculate the monthly rate:
12 0.18 = 0.015
Now put this back into the formula:
A = 200 ( 1 + 0.015 ) 12
Calculate 1 + 0.015 :
1.015
Raise 1.015 to the 12th power:
1.01 5 12 ≈ 1.195618171
Finally, multiply by the principal P :
A = 200 × 1.195618171 ≈ 239.12
Therefore, the total amount of money needed to pay back the loan after 1 year is approximately $239.12 .
