What annual instalment will discharge a debt of Rs.6450 due in 4 years at 5% sim

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Question

What annual instalment will discharge a debt of Rs.6450 due in 4 years at 5% simple interest ?

Options:

A . Rs.1835

B . Rs.1500

C . Rs.1950

D . Rs.1935

Answer: Option B
Answer: (b)Let each instalment be x Then,$(x + {x × 5 × 1}/100) + (x + {x × 5 × 2}/100)$+ $(x + {x × 5 × 3}/100) + x = 6450$$(x + x/20) + (x + x/10)$+ $(x + {3x}/20)$ + x= 6450${21x}/20 + {11x}/10 + {23x}/20 + x = 6450$${21x + 22x + 23x + 20x}/20$= 6450${86x}/20 = 6450$$x = {6450 × 20}/86$ = Rs.1500 Using Rule 10If a sum is to be deposited in equal instalments, then,Equal instalment = ${A × 200}/{T[200 + (T - 1)r]}$where T = no. of years, A = amount, r = Rate of Interest.

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