What annual Instalment will discharge a debt of 7 6450 due in 4 years at 5% simple interest?

25.

The amount to be paid, when principal = ₹ 2,000/-, Rate of simple interest (R) = 5%, T = 2 years, is

₹ 3,200/-
₹ 2,400/-
₹ 2,200/-
₹ 2,200/-

₹ 2,200/-

100 S.I. = PRT
100 x S.I. =

₹ 2,000 x 5 x 2S.I. = ₹ 200/-Required amount = Principal + Interest

= 2000 + 200 = ₹ 2200/-

Correct Answer:

Description for Correct answer:

By using formula, Installment = $ \Large \frac{6450 \times 100}{4 \times 100+ \left(3+2+1\right) } \times 5 $ =$ \Large \frac{6450 \times 100}{4 \times 100+ \left(3+2+1\right) } \times 5 $ =$ \Large \frac{6450 \times 100}{430} $ Installment = Rs.1500 Hence value of installment= Rs.1500

Note: We have explained formula in previous questions.

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Home » Aptitude » Simple interest » Question

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

Let each instalment be y Then,

⇒

y +

y × 5 × 1

y +

y × 5 × 2

y +

y × 5 × 3

+ y = 6450

100

⇒

y +

+ y = 6450

⇒	21y	+	11y	+	23y	+ y = 6450
20	10	20

⇒	21y + 22y + 23y + 20y	= 6450
20

⇒ y =	6450 × 20	= ₹ 1500
86

Second method to solve this question : Here , A = ₹ 6450 , T = 4 years , R = 5%

Equal instalment =	A × 200
T[200 + (T - 1) × R]

Equal instalment =	6450 × 200
4[200 + (4 - 1) × 5]

Equal instalment =	6450 × 200
4 × 215

Equal instalment =	6450 × 200
4 × 215

Equal instalment =	6450 × 50
215

Equal instalment = ₹ 1500

What annual instalment will discharge a debt of 6450 Rs. due in 4 years at 5% simple interest? [A]1500 Rs. [B]1835 Rs. [C]1935 Rs. [D]1950 Rs.

1500 Rs. Let each instalment be x. Then, $latex \because \left ( x+\frac{x\times 5\times 1}{100} \right ) + \left ( x+\frac{x\times 5\times 2}{100} \right ) + \left ( x+\frac{x\times 5\times 3}{100} \right ) + x = 6450&s=1$ $latex => \left ( x+\frac{x}{20} \right )+\left ( x+\frac{x}{10} \right )+\left ( x+\frac{3x}{20} \right )+x = 6450&s=1$ $latex => \frac{21x}{20}+\frac{11x}{10}+\frac{23x}{20}+x = 6450&s=1$ $latex => \frac{21x+22x+23x+20x}{20} = 6450&s=1$ $latex => \frac{86x}{20} = 6450&s=1$ $latex => x = \frac{6450\times 20}{86} = 1500 Rs.&s=1$

Hence option [A] is correct answer.

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Calculation:

Installment for first year = x

Installment for second year = 1.10x

Installment for third year = 1.20x

Installment for third year = 1.30x

Installment for final year = 1.40x

Total amount to be paid = (1 + 1.10 + 1.20 + 1.30 + 1.40) × x = 6450

∴ x = 6450 / 6 = 1075

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