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Thabo starts a small business and takes out a loan of R50 000. He agrees to repay R20 000 at the end of 2 years, and then follow up with another payment of R25 000 one year later. After 5 years he expands his business and takes out an additional loan of R75 000, and agrees to repay R55 000 one year later and the rest of his debt at the end of the third year. If the interest rate is 16% per year compounded annually, calculate the final payment.
in QMI1500 by Diamond (40.2k points) | 16 views

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The future value of the payments at the end of 8 years must be equal to the future value of both loans at the end of 8 years.
Hence, at time T = 8, the future values are calculated using S = P ((1 + R)^T) as follows:
(20 000 (1 + 0.16)^6) + (25 000 (1 + 0.16)^5) + (55 000 (1 + 0.16)^2) + X = (50 000 (1 + 0.16)^8) + (75 000 (1 + 0.16)^3)

(20 000 (1.16)^6) + (25 000 (1.16)^5) + (55 000 (1.16)^2) + X = (50 000 (1.16)^8)
+ (75 000 (1.16)^3)

48 727.93 + 52 508.54 + 74008.00 + X = 163 920.74 + 117 067.20

175 244.47 + X = 280 987.94

X = 280 987.94 – 175 244.47
X = 105 743.47

Hence the final payment is R105 743.47
by Gold Status (10.9k points)

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