Question

in how much time will rs 128000 deposited in a bank at the rate of 7 1/2% p.a compounded annually yield an interest in of rs 32014

Answer 1

Answer:

real answer is 3 years

Answer 2

Given: Principal = Rs. 1,28,000

           Rate of interest = $7\frac{1}{2}$% or 7.5%

           Interest earned = Rs. 32,014

To find: Time in which the given interest has been earned

Solution: Given that,

Principal (P) = Rs. 1,28,000

Rate of interest (r) = 7.5% i.e., 0.075

Interest (I) = Rs. 32,014

Number of conversion periods in a year (m) = 1 (interest compounded annually)

Time (t) = ?

∵ $Interest = Amount - Principal$

and ∵ $Amount = Principal * (1 + \frac{r}{m}) ^{mt}$

So, $Interest = Principal * (1 + \frac{r}{m}) ^{mt} - Principal$

⇒ $32,014 = 128000(1+0.075)^{t} - 128000$      [∵ m = 1]

⇒ $32,014 = 128000[(1+0.075)^{t} - 1]$

⇒ $[(1+0.075)^{t} - 1] = \frac{32014}{128000} = 0.25010$

⇒ $(1+0.075)^{t} = 0.25010 + 1$

⇒ $(1+0.075)^{t} = 1.25010$

Taking log on both sides

⇒ $t \ log (1+0.075) = log \ 1.25010$

⇒ $t \ log (1.075) = log \ 1.25010$

⇒ $t \ * \ 0.03140 = 0.096944$

⇒ $t = \frac{0.096944}{0.03140} = 3.0875 \ ( 3 \ approx.)$

Hence, Rs. 1,28,000 deposited in a bank at the rate of 7.5% p.a.  compounded annually yield an interest of Rs. 32,014 in approximately 3 years.