Question

One person borrows ₹ 4,000 and agrees to repay with a total interest of ₹ 500 in 10 instalments. Each instalment being less than the preceding instalment by ₹ 10. What should be the first and the last instalments?

Answer 1

The instalments are in A. P.

Amount repaid in 10 instalments (S₁₀) = Amount borrowed + total interest

∴ S₁₀ = 4000 + 500 = 4500

Number of instalments (n) = 10

Each instalment is less than the preceding instalment by ₹ 10.

∴ d = – 10

S_n = `"n"/2 [2"a" + ("n" - 1)"d"]`

∴ S₁₀ = `10/2 [2"a" + (10 - 1) (-10)]`

∴ 4500 = 5[2a + 9(–10)]

∴ `4500/5` = 2a – 90

∴ 900 = 2a – 90

∴ 2a = 900 + 90

∴ 2a = 990

∴ a = `990/2`

∴ a = 495

Now, t_n = a + (n – 1)d

∴ t₁₀ = 495 + (10 – 1) (–10)

∴ t₁₀ = 495 + 9(–10)

∴ t₁₀ = 495 – 90

∴ t₁₀ = 405

∴ Amount of the first instalment is 495 and that of the last instalment is 405.