Question

A certain sum of money is invested in two parts at the rate of 16 2/3% per annum compounded annually for 7 years and 10 years respectively. If amount received on both investment is equal. If difference between their investment is 2540. Then find the total investment.

Answer 1

Answer:

15300 Rupees

Step-by-step explanation:

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Answer 2

Answer:

The correct answer to this question is:

the total investment = 11180 ₹

Step-by-step explanation:

Compound Interest:

• In compound interest, the final amount is calculated by adding the interest to the previous year's amount.
• Formula: CI = A - P, where  $A = P (1 + \frac{R}{100})^{t}$

Given,

Rate of interest

R = 50/3 %

R =  (50 / 3) / 100

R = 1 / (3*2)

R = 1 / 6

For 7 years,

A₇ = P₇ ( 1 + 1 / 6 )⁷

A₇ =  P₇ ( 7 / 6 )⁷

For 10 years,

A₁₀ = P₁₀ ( 1 + 1 / 6 )¹⁰

A₁₀ =  P₁₀ ( 7 / 6 )¹⁰

Given A₇ = A₁₀

P₇ ( 7 / 6 )⁷ = P₁₀ ( 7 / 6 )¹⁰

P₇ / P₁₀ = (7 / 3)³

P₇ / P₁₀ = 343 / 216

Using compodendo - dividendo

(P₇ - P₁₀) / (P₇ - P₁₀) = (343 - 216) / (343 + 216)

(P₇ - P₁₀) / (P₇ - P₁₀) = 127 / 559          

Given the difference between their investments as

P₇ - P₁₀ = 2540

P₇ + P₁₀ = x

By substituting the above values, we get

(P₇ - P₁₀) / (P₇ - P₁₀) = 127 / 559

2540 / x = 127 / 559

x = (2540 * 559) / 127

x = 1419860 / 127

x = 11180 ₹

Hence, the total investment = P₇ + P₁₀ = x = 11180 ₹

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