{"id":90556,"date":"2025-06-01T10:30:57","date_gmt":"2025-06-01T10:30:57","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90556"},"modified":"2025-06-01T10:30:57","modified_gmt":"2025-06-01T10:30:57","slug":"a-sum-triples-in-ten-years-under-compound-interest-at-a-certain-rate-o","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-sum-triples-in-ten-years-under-compound-interest-at-a-certain-rate-o\/","title":{"rendered":"A sum triples in ten years under compound interest at a certain rate o"},"content":{"rendered":"

A sum triples in ten years under compound interest at a certain rate of interest, the interest is being compounded annually. In how many years, it would become nine times ?<\/p>\n

[amp_mcq option1=”20 years” option2=”30 years” option3=”40 years” option4=”50 years” correct=”option1″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2020<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
20 years<\/section>\n
Under compound interest, if a principal amount becomes ‘x’ times in ‘T’ years, it will become ‘$x^n$’ times in ‘nT’ years, provided the interest rate and compounding frequency remain constant.<\/section>\n
Let the principal be P and the annual interest rate be r. The amount A after t years is given by $A = P(1+r)^t$.
\nWe are given that the sum triples in ten years:
\n$3P = P(1+r)^{10} \\implies (1+r)^{10} = 3$.
\nWe want to find the number of years ‘t’ it takes for the sum to become nine times the principal:
\n$9P = P(1+r)^t \\implies (1+r)^t = 9$.
\nSince $9 = 3^2$, we can substitute the value of 3 from the first equation:
\n$(1+r)^t = ( (1+r)^{10} )^2$
\n$(1+r)^t = (1+r)^{10 \\times 2}$
\n$(1+r)^t = (1+r)^{20}$
\nEquating the exponents, we get $t = 20$.
\nIt would take 20 years for the sum to become nine times.<\/section>\n","protected":false},"excerpt":{"rendered":"

A sum triples in ten years under compound interest at a certain rate of interest, the interest is being compounded annually. In how many years, it would become nine times ? [amp_mcq option1=”20 years” option2=”30 years” option3=”40 years” option4=”50 years” correct=”option1″] This question was previously asked in UPSC CAPF – 2020 Download PDFAttempt Online 20 … <\/p>\n

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