A start-up company that makes robotic hardware for CIM (computer integrated manufacturing) systems borrowed $1.3 million to expand its packaging and shipping facility. The contract required the company to repay the lender through an innovative mechanism called "faux dividends," a series of uniform annual payments over a fixed period of time. If the company paid $305000 per year for five years, what was the interest rate on the loan?
The interest on the loan was %.
Solving 1300000=305000(1/(1+i)+1/(1+i)^2+1/(1+i)^3+(1+i)^4+(1+i)^5)
Using iterations i=5.6%
Ans: 5.57%
Explanation:
Here, P = 1,300,000
A = 305,000
n = 5
305,000(P/A, i, 5) = 1,300,000
(P/A, i, 5) = 1,300,000 / 305,000 = 4.2623
Firom the interest table we found that the value of (P/A, i, 5) at 5% is 4.3295 and at 6% it is 4.2124. So, by interpolation
i = 5% + [(4.3295 - 4.2623) / 4.3295 - 4.2124)] * (6% - 5%)
= 0.05 + (0.0672 / 0.1171) * 0.01
= 0.0557 or 5.57%
Thus, the interest rate on the loan is 5.57%.
A start-up company that makes robotic hardware for CIM (computer integrated manufacturing) systems borrowed $1.3 million...
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