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Dmitriy789 [7]
3 years ago
6

The sum of three times a and four is the same as five yimes a?

Mathematics
1 answer:
Umnica [9.8K]3 years ago
7 0

\text{the sum of three times a and four}:3a+4\\\\\text{five times a}:5a\\\\The\ equation:\\\\3a+4=5a\qquad\text{subtract 3a from both sides}\\\\4=2a\qquad\text{divide both sides by 2}\\\\2=a\to\boxed{a=2}

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The question is an annuity question with the present value of the annuity given.
The present value of an annuity is given by PV = P(1 - (1 + r/t)^-nt) / (r/t) where PV = $61,600; r = interest rate = 9.84% = 0.0984; t = number of payments in a year = 6; n = number of years = 11 years and P is the periodic payment.
61600 = P(1 - (1 + 0.0984/6)^-(11 x 6)) / (0.0984 / 6)
61600 = P(1 - (1 + 0.0164)^-66) / 0.0164
61600 x 0.0164 = P(1 - (1.0164)^-66)
1010.24 = P(1 - 0.341769) = 0.658231P
P = 1010.24 / 0.658231 = 1534.78
Thus, Niki pays $1,534.78 every two months for eleven years.
The total payment made by Niki = 11 x 6 x 1,534.78 = $101,295.48
Therefore, interest paid by Niki = $101,295.48 - $61,600 = $39,695.48
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