document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176049>Question 1176049</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850587 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=850587\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down this loan problem step-by-step.\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.\r<BR>\n" );
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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( "1.  **Monthly Interest Rate:**<BR>\n" );
document.write( "    * Since the loan is repaid monthly, we need to find the monthly interest rate.<BR>\n" );
document.write( "    * Monthly interest rate (i) = Annual interest rate / 12<BR>\n" );
document.write( "    * i = 0.24 / 12 = 0.02 (or 2%)\r<BR>\n" );
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document.write( "2.  **Loan Term in Months:**<BR>\n" );
document.write( "    * The loan term is 3 months (n = 3).\r<BR>\n" );
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document.write( "3.  **Upfront Interest (Compulsory Saving):**<BR>\n" );
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\r<BR>\n" );
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document.write( "4.  **Effective Loan Amount:**<BR>\n" );
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\r<BR>\n" );
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document.write( "5.  **Monthly Payment (PMT) Using Reducing Balance Method:**<BR>\n" );
document.write( "    * We can use the loan payment formula:<BR>\n" );
document.write( "        * PMT = P * [i(1 + i)^n] / [(1 + i)^n - 1]<BR>\n" );
document.write( "    * Where:<BR>\n" );
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]<BR>\n" );
document.write( "    * PMT = 18,800,000 * [0.02(1.02)^3] / [(1.02)^3 - 1]<BR>\n" );
document.write( "    * PMT = 18,800,000 * [0.02(1.061208)] / [1.061208 - 1]<BR>\n" );
document.write( "    * PMT = 18,800,000 * [0.02122416] / [0.061208]<BR>\n" );
document.write( "    * PMT = 18,800,000 * 0.346757<BR>\n" );
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( "1.  **Total Amount Paid:**<BR>\n" );
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\r<BR>\n" );
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document.write( "2.  **Total Interest Paid:**<BR>\n" );
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\r<BR>\n" );
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document.write( "3.  **Actual interest rate.**<BR>\n" );
document.write( "    * Total interest = 754,094.80<BR>\n" );
document.write( "    * Total amount received = 18,800,000<BR>\n" );
document.write( "    * Percentage of interest = (754,094.80/18,800,000)*100 = 4.01%<BR>\n" );
document.write( "    * 4.01% for 3 months.<BR>\n" );
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%.<BR>\n" );
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