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 May 16th, 2018, 01:34 AM #1 Senior Member   Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry Ask About Annuity Mr. Budi borrows 2,000,000IDR which will be amortized with 10 annuities. The first annuity will be paid in 1 year with 10% per year interest. Make the installment plan! For the annuity I got A = $\displaystyle M\times\frac1{\sum_{n=1}^p(1+i)^{-n}}$ = $\displaystyle 2,000,000\times\frac1{\sum_{n=1}^{10}(1+0,1)^{-n}}$ = $\displaystyle 2,000,000\times\frac1{\sum_{n=1}^{10}(1,1)^{-n}}$ = $\displaystyle 2,000,000\times\frac1{\sum_{n=1}^{10}(1,1)^{-n}}$ = $\displaystyle 2,000,000\times\frac1{(1,1)^{-1}+(1,1)^{-2}+(1,1)^{-3}+(1,1)^{-4}+(1,1)^{-5}+(1,1)^{-6}+(1,1)^{-7}+(1,1)^{-8}+(1,1)^{-9}+(1,1)^{-10}}$ ($\displaystyle (1,1)^{-1} + (1,1)^{-2} + … + (1,1)^{-10}$ is a geometric sequence with the first term $\displaystyle a = (1,1)^{-1}$ and ratio $\displaystyle r = (1,1)^{-1}$) = $\displaystyle 2,000,000\times\frac1{\frac{1-1.1^{-10}}{0.1}}$ = $\displaystyle 2,000,000\times\frac{0.1}{1-1.1^{-10}}$ = 2,000,000 × 0.61445671 = 1,228,913.42 Thus, the annuity is 1,228,913.42. On the end of first year: Annuity = 1,228,913.42IDR Interest : 10% × 2,000,000IDR = 200,000IDR Installment : 1,228,913.42IDR – 200.000IDR = 1,028,913.42IDR Remaining loan : 2,000,000IDR – 1,028,913.42IDR = 971,086.58IDR On the end of second year: Annuity = 1,228,913.42IDR Interest : 10% × 971,086.58IDR = 97,108.66IDR Installment : 1,228,913.42IDR – 97,108.66IDR = 1,131,804.76IDR Remaining loan : 971,086.58IDR – 1,131,804.76IDR = -159.718,58IDR Why am I seeing negatives already? Last edited by Monox D. I-Fly; May 16th, 2018 at 01:40 AM. May 16th, 2018, 04:50 AM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Geezzzz Mr.Fly...your post gave me a headache! Your problem is: 2000000 is borrowed at rate of 10% APR, over 10 years. Calculate the annual payment. Formula: P = A*i / (1 - v) where v = 1 / (1 + i)^n A = amount borrowed = 2000000 i = interest rate = .10 n = number of payments = 10 P = payment amount = ? That'll give you P = 325490.79 The formula is of course the result of a geometric sequence: present value of payments = 2000000 or future value of payments = 2000000*1.10^10 Your loan statement will look like: Code: year payment interest balance 0 2000000.00 1 325490.79 200000.00 1874509.21 2 325490.79 187450.92 1736469.34 ... 9 325490.79 56490.14 295900.72 10 325490.79 29590.07 .00 Thanks from jonah Tags annuity Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Denis Economics 2 June 7th, 2015 06:31 AM Yume Economics 1 May 4th, 2015 09:34 PM Surfboard Economics 8 March 7th, 2015 09:45 AM fatim Economics 6 November 30th, 2014 07:20 PM simplequestion Economics 3 October 8th, 2008 12:41 PM

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