Manually calculate the compound interest on a 13% loan of $1,600 for three years if the interest is compounded annually.
1600((1+.13)^3-1)
707.64
To manually calculate compound interest, we use the formula:
A = P(1 + r/n)^(nt)
where:
A = the future value of the investment/loan, including interest
P = the principal amount (initial investment/loan amount)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case:
P = $1,600
r = 13% = 0.13 (as a decimal)
n = 1 (compounded annually)
t = 3 years
Substituting these values into the formula, we get:
A = 1600(1 + 0.13/1)^(1*3)
= 1600(1 + 0.13)^3
= 1600(1.13)^3
Now, let's calculate the compound interest step by step.
Step 1: Calculate the parentheses portion
(1 + 0.13)^3
= (1 + 0.13) * (1 + 0.13) * (1 + 0.13)
= 1.13 * 1.13 * 1.13
= 1.419857
Step 2: Multiply the result from step 1 with the principal amount (P)
1600 * 1.419857
= 2,271.79
Step 3: Subtract the principal amount (P) from the result obtained in step 2 to find the compound interest
2,271.79 - 1600
= 671.79
Therefore, the compound interest on a 13% loan of $1,600 for three years, compounded annually, is $671.79.
To manually calculate compound interest, you can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal amount (the initial amount before interest)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In your case, the principal amount (P) is $1,600, the annual interest rate (r) is 13% expressed as 0.13, the number of times interest is compounded per year (n) is 1 (since it's compounded annually), and the number of years (t) is 3.
Now let's substitute these values into the formula to calculate the compound interest manually:
A = 1600(1 + 0.13/1)^(1*3)
= 1600(1 + 0.13)^3
= 1600(1.13)^3
≈ 1600(1.42)
≈ $2,272
So, the compound interest on a 13% loan of $1,600 for three years, compounded annually, is approximately $672 ($2,272 - $1,600).