Question : A sum invested at a certain rate of interest per annum, compounded annually, amounts to INR 3,600 in 2 years and to INR 6,480 in 4 years. What is the sum invested?
Option 1: INR 2,500
Option 2: INR 2,000
Option 3: INR 2,400
Option 4: INR 3,600
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Correct Answer: INR 2,000
Solution : Use: Amount = $P×(1+\frac{r}{n})^{nt}$ where, $P$ is the principal amount (the initial sum invested), $r$ is the annual interest rate (as a decimal), $n$ is the number of times interest is compounded per year, and $t$ is the time in years. For interest to be compounded annually, n = 1 After 2 years, the amount is 3,600 So, 3,600 = $P×(1+\frac{r}{1})^{1×2}$ = $P(1+r)^{2}$ After 4 years, the amount is 6,480 So, 6,480 = $P×(1+\frac{r}{1})^{1×4}$ = $P(1+r)^{4}$ Now, ⇒ $\frac{P(1+r)^{4}}{P(1+r)^{2}}$ = $\frac{6480}{3600}$ ⇒ $(1+r)^{2} = \frac{6480}{3600}$ ⇒ $(1+r)^{2} = \frac{18}{10}$ ⇒ $(1+r)^{2}$ = 1.8 So,$P$ (1 + $r$)2 = 3,600 ⇒ $P$ × 1.8 = 3600 ⇒ $P$ = $\frac{3600}{1.8}$ ⇒ $P$ = 2000 Hence, the correct answer is INR 2,000.
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Question : A sum invested at a certain rate of interest per annum, compounded annually, amounts to INR 14,400 in 2 years and to INR 25,920 in 4 years. What is the sum invested?
Option 1: INR 8,200
Option 2: INR 7,500
Option 3: INR 8,500
Option 4: INR 8,000
Question : A certain sum of money amounts to 3 times itself in 13 years when interest is compounded annually at a certain interest rate per annum. In how many years will the initial sum amount to 9 times itself at the same interest rate per annum, also compounded annually?
Option 1: 32 years
Option 2: 26 years
Option 3: 30 years
Option 4: 20 years
Question : At a certain rate of interest per annum, compounded annually, a certain sum of money amounts to two times itself in 11 years. In how many years will the sum of money amount to four times itself at the previous rate of interest per annum, also compounded annually?
Option 1: 20 years
Option 2: 5.5 years
Option 3: 22 years
Option 4: 33 years
Question : A sum, when invested for 2 years at the rate of 10% per annum at simple interest, amounts to INR 4,800 on maturity. What is the sum invested?
Option 1: INR 3,600
Option 2: INR 4,000
Option 3: INR 3,500
Option 4: INR 4,200
Question : A sum of money, invested at a certain rate of simple interest per annum, amounts to INR 720 in 4 years and to INR 800 in 5 years. The sum invested is:
Option 1: INR 400
Option 2: INR 600
Option 3: INR 500
Option 4: INR 360
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