Suppose you take a loan of $1000 today at a compound interest of 10 percent. Calculate the loan amount at the end of year 2.
Thanks!!!
Do you mean what do you owe?
1000 * 1.10 * 1.10
I believe it’s asking how much the loan amount becomes after the interest is applied. The options are:
$1210
$1100
$1215
$1000
Thank you!!
To calculate the loan amount at the end of year 2 with compound interest, we can use the formula:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount
P = the principal amount (loan amount)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case:
P = $1000 (loan amount)
r = 10% (interest rate, expressed as a decimal, so 0.10)
n = 1 (since the interest is compounded annually)
t = 2 (years)
Plugging the values into the formula:
A = $1000(1 + 0.10/1)^(1*2)
A = $1000(1 + 0.10)^2
A = $1000(1.10)^2
A = $1000(1.21)
A ≈ $1210
So, the loan amount at the end of year 2 with compound interest would be approximately $1210.
To calculate the loan amount at the end of year 2, we need to apply the compound interest formula:
A = P * (1 + r)^n
Where:
A = loan amount at the end of year 2
P = initial loan amount
r = interest rate per period (in this case, per year)
n = number of periods (in this case, 2 years)
In your case, the initial loan amount (P) is $1000 and the interest rate (r) is 10% or 0.10. We want to find out the loan amount at the end of year 2 (A) after 2 periods (n).
Plugging these values into the formula, we have:
A = $1000 * (1 + 0.10)^2
Simplifying this equation, we get:
A = $1000 * (1.10)^2
A = $1000 * 1.21
A = $1210
Therefore, the loan amount at the end of year 2 will be $1210.