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Sebuah pinjaman sebesar yang harus dilunasi dengan 6 anuitas. Jika besar bunga perbulan dan pembayaran pertama dilakukan setelah sebulan sisa hutang pada akhir bulan ke-5 adalah ....

Sebuah pinjaman sebesar size 14px Rp size 14px space size 14px 750 size 14px. size 14px 000 size 14px. size 14px 000 size 14px comma size 14px 00 yang harus dilunasi dengan 6 anuitas. Jika besar bunga begin mathsize 14px style 4 percent sign end style perbulan dan pembayaran pertama dilakukan setelah sebulan sisa hutang pada akhir bulan ke-5 adalah ....

Jawaban:

Dengan menerapkan rumus dan konsep ANUITAS:

Diketahui:

Pinjaman begin mathsize 14px style left parenthesis straight M right parenthesis equals Rp space 750.000.000 comma 00 end style 

Bunga begin mathsize 14px style left parenthesis i right parenthesis equals 4 percent sign end style 

Banyak Anuitas begin mathsize 14px style left parenthesis straight n right parenthesis equals 6 end style 

Ditanya:

Anuitas begin mathsize 14px style left parenthesis straight A right parenthesis end style, Sisa hutang akhir bulan ke-5 (setelah pembayaran ke-4).

Solusi:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight A equals cell fraction numerator straight M times straight i over denominator 1 minus left parenthesis 1 plus straight i right parenthesis to the power of negative straight n end exponent end fraction end cell row blank equals cell fraction numerator Rp space 750.000.000 times 4 percent sign over denominator 1 minus left parenthesis 1 plus 4 percent sign right parenthesis to the power of negative 6 end exponent end fraction end cell row blank equals cell fraction numerator Rp space 750.000.000 times left parenthesis begin display style 4 over 100 end style right parenthesis over denominator 1 minus left parenthesis 104 over 100 right parenthesis to the power of negative 6 end exponent end fraction end cell row blank equals cell fraction numerator Rp space 750.000.000 times left parenthesis begin display style 1 over 25 end style right parenthesis over denominator 1 minus left parenthesis 1 comma 04 right parenthesis to the power of negative 6 end exponent end fraction end cell row blank equals cell fraction numerator Rp space 30.000.000 over denominator 1 minus 0 comma 7903145257 end fraction end cell row blank equals cell fraction numerator Rp space 30.000.000 over denominator 0 comma 2096854743 end fraction end cell row blank equals cell Rp space 143.071.426 comma 90 end cell end table end style 

Jadi, Anuitas begin mathsize 14px style left parenthesis straight A right parenthesis equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 143 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 071 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 426 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 90 end table end style.

Untuk menentukan sisa Pinjaman, gunakan rumus:

begin mathsize 14px style straight S subscript straight m equals straight b subscript straight m plus 1 end subscript over straight i end style 

Angsuran ke lima begin mathsize 14px style straight a subscript 5 end style:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight a subscript straight n end cell equals cell left parenthesis straight A minus straight i times straight M right parenthesis left parenthesis 1 plus straight i right parenthesis to the power of straight n minus 1 end exponent space end cell row cell a subscript 5 end cell equals cell left parenthesis Rp space 143.071.426 comma 9 minus 4 percent sign times Rp 750.000.000 right parenthesis left parenthesis 1 plus 4 percent sign right parenthesis to the power of 5 minus 1 end exponent end cell row blank equals cell left parenthesis Rp space 143.071.426 comma 9 minus 4 over 100 times Rp 750.000.000 right parenthesis left parenthesis 1 plus 4 over 100 right parenthesis to the power of 4 end cell row blank equals cell left parenthesis Rp space 143.071.426 comma 9 minus 1 over 25 times Rp 750.000.000 right parenthesis left parenthesis 104 over 100 right parenthesis to the power of 4 end cell row blank equals cell left parenthesis Rp space 143.071.426 comma 9 minus Rp 30.000.000 right parenthesis left parenthesis 1 comma 04 right parenthesis to the power of 4 end cell row blank equals cell left parenthesis Rp space 113.071.426 comma 9 right parenthesis left parenthesis 1 comma 169858565 right parenthesis end cell row blank equals cell Rp space 132.277.576 comma 70 end cell end table end style  

Anuitas terdiri atas angsuran dan bunga, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight A equals cell straight a subscript straight n plus straight b subscript straight n end cell row straight A equals cell straight a subscript 5 plus straight b subscript 5 end cell row cell straight b subscript 5 end cell equals cell straight A minus straight a subscript 5 end cell row cell straight b subscript 5 end cell equals cell Rp space 143.071.426 comma 90 minus Rp 132.277.576 comma 7 end cell row cell straight b subscript 5 end cell equals cell Rp space 10.793.850 comma 2 end cell end table end style 

Sisa pinjaman pada akhir bulan ke lima (begin mathsize 14px style S subscript 4 end style) adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight S subscript 4 end cell equals cell straight b subscript 4 plus 1 end subscript over straight i end cell row blank equals cell fraction numerator straight b subscript 5 over denominator 4 percent sign end fraction end cell row blank equals cell fraction numerator Rp space 10.793.850 comma 2 over denominator 0 comma 04 end fraction end cell row blank equals cell Rp space 269.846.255 end cell end table end style   

Jadi, Sisa pinjaman pada akhir bulan ke lima (begin mathsize 14px style S subscript 4 end style) adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 269 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 846 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 255 end table comma 00 end style.

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