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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 $\displaystyle r = (1,1)^{1}$) = $\displaystyle 2,000,000\times\frac1{\frac{11.1^{10}}{0.1}}$ = $\displaystyle 2,000,000\times\frac{0.1}{11.1^{10}}$ = 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. IFly; May 16th, 2018 at 01:40 AM. 
May 16th, 2018, 04:50 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,148 Thanks: 1004 
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 

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