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?
2 answers
,llobohvikh
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.
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.
1 answer