Monoxdifly
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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 = [math]M\times\frac1{\sum_{n=1}^p(1+i)^{-n}}[/math] = [math]2,000,000\times\frac1{\sum_{n=1}^{10}(1+0,1)^{-n}}[/math] = [math]2,000,000\times\frac1{\sum_{n=1}^{10}(1,1)^{-n}}[/math] = [math]2,000,000\times\frac1{\sum_{n=1}^{10}(1,1)^{-n}}[/math] = [math]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}}[/math]
([math](1,1)^{-1} + (1,1)^{-2} + … + (1,1)^{-10}[/math] is a geometric sequence with the first term [math]a = (1,1)^{-1}[/math] and ratio [math]r = (1,1)^{-1}[/math])
= [math]2,000,000\times\frac1{\frac{1-1.1^{-10}}{0.1}}[/math] = [math]2,000,000\times\frac{0.1}{1-1.1^{-10}}[/math] = 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?
For the annuity I got A = [math]M\times\frac1{\sum_{n=1}^p(1+i)^{-n}}[/math] = [math]2,000,000\times\frac1{\sum_{n=1}^{10}(1+0,1)^{-n}}[/math] = [math]2,000,000\times\frac1{\sum_{n=1}^{10}(1,1)^{-n}}[/math] = [math]2,000,000\times\frac1{\sum_{n=1}^{10}(1,1)^{-n}}[/math] = [math]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}}[/math]
([math](1,1)^{-1} + (1,1)^{-2} + … + (1,1)^{-10}[/math] is a geometric sequence with the first term [math]a = (1,1)^{-1}[/math] and ratio [math]r = (1,1)^{-1}[/math])
= [math]2,000,000\times\frac1{\frac{1-1.1^{-10}}{0.1}}[/math] = [math]2,000,000\times\frac{0.1}{1-1.1^{-10}}[/math] = 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?
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