17
A sum of money doubles itself in 6 years at a certain rate of compound interest. In how many years will be 16 times at the same rate of interest?
- A18 years
- B24 years
- C30 years
- D12 years
Answer not set
Discussion 1
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CCommunity
Let the sum be ‘x’ and the rate be ‘r’
∴ According to the 1st given condition,
⇒ ?$(2x\; = \;x{\left. {\left( {1\; + \;\frac{r}{{100}}} \right.} \right)^6})$
$(\therefore {\left( {1 + r/100} \right)^6} = 2)$ ----(1)
For the 2ndcondition, Let t be the number of years required
$(16x\; = \;x{\left. {\left( {1\; + \;\frac{r}{{100}}} \right.} \right)^t})$
⇒? $(16\; = \;{\left. {\left( {1\; + \;\frac{r}{{100}}} \right.} \right)^t})$
⇒ ?$( {2^4} = {\left( {{{\left( {1 + r/100} \right)}^6}} \right)^4})$ from ----(1)
$(\therefore {\left( {1 + r/100} \right)^t} = {\left( {1 + r/100} \right)^{24}})$
∴ t = 24
∴ The amount will become 16 times in 24 years.
∴ According to the 1st given condition,
⇒ ?$(2x\; = \;x{\left. {\left( {1\; + \;\frac{r}{{100}}} \right.} \right)^6})$
$(\therefore {\left( {1 + r/100} \right)^6} = 2)$ ----(1)
For the 2ndcondition, Let t be the number of years required
$(16x\; = \;x{\left. {\left( {1\; + \;\frac{r}{{100}}} \right.} \right)^t})$
⇒? $(16\; = \;{\left. {\left( {1\; + \;\frac{r}{{100}}} \right.} \right)^t})$
⇒ ?$( {2^4} = {\left( {{{\left( {1 + r/100} \right)}^6}} \right)^4})$ from ----(1)
$(\therefore {\left( {1 + r/100} \right)^t} = {\left( {1 + r/100} \right)^{24}})$
∴ t = 24
∴ The amount will become 16 times in 24 years.