In 9 years, Rollo Company will have to repay a $100,000 loan. Assume a 6% interest rate compounded quarterly. How much must Rollo Company pay each period to have $100,000 at the end of 9 years?
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To find the amount that Rollo Company must pay each period, we can use the formula for the future value of an annuity:
FV = PMT x ((1 + r/n)^(n*t) - 1) / (r/n)
where FV is the future value (which we want to be $100,000), PMT is the payment per period, r is the annual interest rate (6%), n is the number of periods per year (4 for quarterly), and t is the total number of periods (9 years x 4 quarters per year = 36 periods).
Plugging in these values, we get:
100,000 = PMT x ((1 + 0.06/4)^(4*36) - 1) / (0.06/4)
Simplifying, we get:
100,000 = PMT x (1.06^36 - 1) / 0.015
100,000 = PMT x 49.3039
Dividing both sides by 49.3039, we get:
PMT = 100,000 / 49.3039
PMT ≈ $2,028.69
Therefore, Rollo Company must pay approximately $2,028.69 per quarter in order to have $100,000 at the end of 9 years.
To find out how much Rollo Company must pay each period to have $100,000 at the end of 9 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = 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, the final amount A is the desired value of $100,000, the principal amount P is the loan amount, the annual interest rate r is 6% (or 0.06), the number of times interest is compounded per year n is 4 (quarterly), and the number of years t is 9.
The equation becomes:
100,000 = P(1 + 0.06/4)^(4*9)
Now, we can rearrange the equation to solve for P (the periodic payment amount):
P = 100,000 / (1 + 0.06/4)^(4*9)
Calculating this equation will give us the periodic payment amount that Rollo Company must pay to have $100,000 at the end of 9 years.
To find out how much Rollo Company must pay each period to have $100,000 at the end of 9 years with a 6% interest rate compounded quarterly, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A = the future value of the loan (which is $100,000)
P = the principal amount of the loan (unknown)
r = the annual interest rate (6% or 0.06)
n = the number of times interest is compounded per year (quarterly, so 4)
t = the number of years (9)
We need to solve for P, the principal amount, so we'll rearrange the formula:
P = A / (1 + r/n)^(nt)
Now let's substitute the known values into the formula:
P = $100,000 / (1 + 0.06/4)^(4*9)
Calculating inside the parentheses:
P = $100,000 / (1 + 0.015)^(36)
Now we can simplify the equation:
P = $100,000 / (1.015)^(36)
Using a calculator or spreadsheet, calculate:
P ≈ $100,000 / (1.641)
Therefore, Rollo Company must pay approximately $60,887.38 each period to have $100,000 at the end of 9 years.