Lee Willis loaned Audrey Chin $16000 to open Snip Its Hair Salon. After 6 years, Audrey will repay Lee with 8% interest compounded quartly. How much will Lee receive at the end of 6 years?
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To calculate the amount Lee will receive at the end of 6 years with 8% interest compounded quarterly, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future amount
P = the principal amount (initial loan)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $16,000
r = 8% or 0.08 (converted to decimal)
n = 4 (quarterly compounding)
t = 6 years
Plugging the values into the formula:
A = 16000(1 + 0.08/4)^(4 * 6)
Simplifying:
A = 16000(1 + 0.02)^24
A = 16000(1.02)^24
Calculating:
A ≈ $25,371.33
Therefore, Lee will receive approximately $25,371.33 at the end of 6 years.
To calculate the amount that Lee will receive at the end of 6 years with 8% interest compounded quarterly, we need to use the compound interest formula. The formula is as follows:
A = P * (1 + r/n)^(n*t)
Where:
A = the final amount (what Lee will receive at the end)
P = principal amount (the initial loan amount)
r = annual interest rate (in decimal form, 8% = 0.08)
n = number of times the interest is compounded per year (quarterly = 4 times)
t = number of years
Given:
P = $16,000
r = 8% = 0.08
n = 4 (quarterly)
t = 6 years
Using the formula, we substitute these values into the equation:
A = $16,000 * (1 + 0.08/4)^(4*6)
Now, we can solve this equation to find the final amount that Lee will receive.
P = Po(1+r)^n.
r = (8$/4)/100% = 0.02 = Quarterly % rate expressed as a decimal.
n = 4comp/yr * 6yrs. = 24 Compounding
periods.
Solve the given Eq for P.
Answer: $25,735.00.