A finance company declares that, at a certain compound interest rate, a sum of money deposited by anyone will become 8 times in 3 years. If the same amount is deposited at the same compound rate of interest, then in how many years will it become 16 times?

dsuc.created: 2 years ago | dsuc.updated: 1 year ago

dsuc.updated: 1 year ago

$L e t, p r i n c i p a l a m o u n t o f x; a n d r a t e o f c o m p o u n d i n t e r e s t b e r; t i m e, n = ? a p p l y t h e l a w o f c o m p o u n d i n t e r e s t, w e c a n w r i t e x {(1 + \frac{r}{100})}^{3} = 8 x = {(1 + \frac{r}{100})}^{3} = \frac{8 x}{x} = 8 ∴ {(1 + \frac{r}{100})}^{3} = 8 . . . . . . . . . . . . . . . . . . . . (i) N o w, a c c o r d i n g t o q u e s t i o n, x {(1 + \frac{r}{100})}^{n} = 16 x = {(1 + \frac{r}{100})}^{n} = 16 = {(1 + \frac{r}{100})}^{n} = 2^{4} = (1 + \frac{r}{100}) = 2^{(3 \times \frac{4}{3})} = {(1 + \frac{r}{100})}^{n} = 8^{\frac{4}{3}} = {{(1 + \frac{r}{100})}^{3}}^{\frac{n}{3}}^{3}}^{\frac{4}{3}} = \frac{n}{3} = \frac{4}{3} ∴ n = 4$