A sum of rs400 amounts to rs480 in 4years. What will it amount to if the rate of interest is increased by 2% p.a
let the current rate be i where i is a decimal
e.g. 5% = .05 = i
at the current rate:
400(1+i)^4 = 480
(1+i)^4 = 1.2
take 4th root of both sides
1+i = 1.046635..
i = .046635..
at new rate i = .066635....
amount = 400(1.066635...)^4
= ....
Madharchod SIMple interest h
To calculate the amount, we need to use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = final amount
P = principal amount (initial sum of money)
r = rate of interest
n = number of times interest is compounded per year
t = time in years
In this case, P = rs400, t = 4 years, and the rate of interest is increased by 2% p.a. We will consider the original rate of interest as r.
First, let's find the value of r. We know that:
A = rs480
P = rs400
t = 4 years
Using the formula, we can solve for r:
A = P * (1 + r/n)^(n*t)
480 = 400 * (1 + r/100)^(1*4)
Simplifying the equation:
1.2 = (1 + r/100)^4
Taking the fourth root of both sides:
(1 + r/100) = ∛1.2
1 + r/100 = 1.09139 (rounding to 5 decimal places)
Subtracting 1 from both sides:
r/100 = 0.09139
Multiplying both sides by 100:
r = 9.139
So, the original rate of interest is 9.139%.
Now, we can calculate the amount with the increased interest rate:
r_2 = r + 2
r_2 = 9.139 + 2 = 11.139
Using the new rate of interest (11.139%) and the values of P, t from our earlier calculation, we can find the new amount:
A_new = P * (1 + r_2/100)^(1*4)
A_new = 400 * (1 + 11.139/100)^(4)
A_new = 400 * 1.11139^4
A_new = 400 * 1.492853
Calculating this:
A_new = rs597.14
Therefore, if the rate of interest is increased by 2% p.a., the amount will be rs597.14.