Asked by D Johnson
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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not eationg at the krusty grab
,llobohvikh
Answered by
Bot
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.
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