{"id":37203,"date":"2024-06-17T06:32:37","date_gmt":"2024-06-17T06:32:37","guid":{"rendered":"https:\/\/www.greatassignmenthelp.com\/questions\/?p=37203"},"modified":"2024-06-17T06:32:55","modified_gmt":"2024-06-17T06:32:55","slug":"what-is-the-compound-interest-on-a-three-year-100-00-loan-at-a-10-percent-annual-interest-rate","status":"publish","type":"post","link":"https:\/\/www.greatassignmenthelp.com\/questions\/what-is-the-compound-interest-on-a-three-year-100-00-loan-at-a-10-percent-annual-interest-rate\/","title":{"rendered":"What is the compound interest on a three-year, $100.00 loan at a 10 percent annual interest rate?"},"content":{"rendered":"
What is the compound interest on a three-year, $100.00 loan at a 10 percent annual interest rate?<\/p>\n
a. $10.00<\/p>\n
b. $21.00<\/p>\n
c. $33.10<\/p>\n
d. $46.41<\/p>\n
Answer: c. $33.10<\/strong><\/p>\n
To compute the total interest compounded on it for three years, we have $100.00 loan at a 10% annual interest rate, we can use the compound interest formula:<\/p>\n
A = P(1 + r\/n)^(nt)<\/p>\n
Where:<\/p>\n
A = Final amount (principal + interest)<\/p>\n
P = Initial principal amount<\/p>\n
r = Annual interest rate (in decimal form)<\/p>\n
n = Number of times the interest is compounded per year (for annual compounding, n = 1)<\/p>\n
t = time in years<\/p>\n
Given:<\/p>\n
P = $100.00<\/p>\n
r = 0.10 (10% expressed in decimal form)<\/p>\n
n = 1 (for annual compounding)<\/p>\n
t = 3 years<\/p>\n
Substituting the values in the formula:<\/p>\n
A = 100(1 + 0.10\/1)^(1 * 3)<\/p>\n
A = 100(1.10)^3<\/p>\n
A = 100 *(1.331)<\/p>\n
A = $133.10<\/p>\n
Since the initial principal amount was $100, the compound interest earned over three years is:<\/p>\n