document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175997>Question 1175997</A>: <I><SPAN STYLE=\"word-break: break-all;\"> John,a client of UMOJA microfinance institution took a loan of TZS 20000000 on 2 January 2018 which charges 24% interest per annum.using reducing balance method.the loan contract indicated that the loan was supposed to be repaid in 3 months period on loan is to be charged upfront as compulsory saving.required<BR>\n" );
document.write( "(a) calculate the total payment (PMT) made each period by the client.<BR>\n" );
document.write( "(b) determine the interest which a client is actually paying. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850598 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You've asked this question before, and I provided a detailed solution. Let's reiterate it for clarity.\r<BR>\n" );
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document.write( "Given Information:\r<BR>\n" );
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document.write( "Loan amount (Principal, P): TZS 20,000,000<BR>\n" );
document.write( "Annual interest rate (r): 24% (0.24)<BR>\n" );
document.write( "Loan term: 3 months<BR>\n" );
document.write( "Interest charged upfront as compulsory savings.<BR>\n" );
document.write( "Calculations:\r<BR>\n" );
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document.write( "(a) Calculate the total payment (PMT) made each period by the client.\r<BR>\n" );
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document.write( "Monthly Interest Rate:\r<BR>\n" );
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document.write( "Monthly interest rate (i) = Annual interest rate / 12<BR>\n" );
document.write( "i = 0.24 / 12 = 0.02 (or 2%)<BR>\n" );
document.write( "Loan Term in Months:\r<BR>\n" );
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document.write( "The loan term is 3 months (n = 3).<BR>\n" );
document.write( "Upfront Interest (Compulsory Saving):\r<BR>\n" );
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document.write( "The interest for the entire loan period is charged upfront.<BR>\n" );
document.write( "Total interest = P * i * n = 20,000,000 * 0.02 * 3 = TZS 1,200,000<BR>\n" );
document.write( "Effective Loan Amount:\r<BR>\n" );
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document.write( "The amount the client effectively receives is the original loan amount minus the upfront interest.<BR>\n" );
document.write( "Effective loan amount = 20,000,000 - 1,200,000 = TZS 18,800,000<BR>\n" );
document.write( "Monthly Payment (PMT) Using Reducing Balance Method:\r<BR>\n" );
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document.write( "We can use the loan payment formula:\r<BR>\n" );
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document.write( "PMT = P * [i(1 + i)^n] / [(1 + i)^n - 1]<BR>\n" );
document.write( "Where:\r<BR>\n" );
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document.write( "PMT = Monthly payment<BR>\n" );
document.write( "P = Effective loan amount (TZS 18,800,000)<BR>\n" );
document.write( "i = Monthly interest rate (0.02)<BR>\n" );
document.write( "n = Number of months (3)<BR>\n" );
document.write( "PMT = 18,800,000 * [0.02(1 + 0.02)^3] / [(1 + 0.02)^3 - 1]\r<BR>\n" );
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document.write( "PMT = 18,800,000 * [0.02(1.02)^3] / [(1.02)^3 - 1]\r<BR>\n" );
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document.write( "PMT = 18,800,000 * [0.02(1.061208)] / [1.061208 - 1]\r<BR>\n" );
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document.write( "PMT = 18,800,000 * [0.02122416] / [0.061208]\r<BR>\n" );
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document.write( "PMT = 18,800,000 * 0.346757\r<BR>\n" );
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document.write( "PMT = 6,518,031.6\r<BR>\n" );
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document.write( "Therefore, the monthly payment is approximately TZS 6,518,031.60\r<BR>\n" );
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document.write( "(b) Determine the interest which a client is actually paying.\r<BR>\n" );
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document.write( "Total Amount Paid:\r<BR>\n" );
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document.write( "Total amount paid = Monthly payment * Number of months<BR>\n" );
document.write( "Total amount paid = 6,518,031.6 * 3 = TZS 19,554,094.80<BR>\n" );
document.write( "Total Interest Paid:\r<BR>\n" );
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document.write( "Total interest paid = Total amount paid + Upfront interest - Original loan amount.<BR>\n" );
document.write( "Total interest paid = 19,554,094.80 + 1,200,000 - 20,000,000<BR>\n" );
document.write( "Total interest paid = 754,094.80<BR>\n" );
document.write( "Actual interest rate.\r<BR>\n" );
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document.write( "Total interest = 754,094.80\r<BR>\n" );
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document.write( "Total amount received = 18,800,000\r<BR>\n" );
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document.write( "Percentage of interest = (754,094.80/18,800,000)*100 = 4.01%\r<BR>\n" );
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document.write( "4.01% for 3 months.\r<BR>\n" );
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document.write( "Annual interest rate = 4.01%*4 = 16.04%\r<BR>\n" );
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document.write( "The client is actually paying TZS 754,094.80 in interest on top of the upfront interest, and the actual annual interest rate is 16.04%.\r<BR>\n" );
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document.write( "Answers:\r<BR>\n" );
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document.write( "(a) Total payment (PMT) made each period: Approximately TZS 6,518,031.60<BR>\n" );
document.write( "(b) Interest which a client is actually paying: TZS 754,094.80 and the actual annual interest rate is 16.04%. </SPAN>\n" );
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