A sum of ₹400 amounts to ₹480 in 4 years.What will it amount to, if the rate of interest is increased by 2%p.a.?
if compound interest,
400(1+r)^4 = 480
(1+r)^4 = 1.2
r = .0466
Is your new r
(r + .02)=.0666
or is it
9*1.02 = .0475
??
Do a similar calculation if simple interest.
400(1+i)^2 = 480
(1+i)^2 = 1.2
1+i = 1.095445
i = .095445
new rate = .095445 + .02 = .115445
new amount = 400(1.115445)^2 = 497.69
Please teach me
To calculate the amount after a change in the interest rate, we need to determine the new rate of interest.
Let's start by finding the rate of interest for the initial investment.
In the given scenario, a sum of ₹400 amounting to ₹480 in 4 years indicates a simple interest model. The formula to calculate simple interest is:
Simple Interest (SI) = Principal (P) * Rate of Interest (R) * Time (T)
Using the given information, we can calculate the rate of interest as follows:
480 = 400 + (400 * R * 4)
To isolate the rate (R), we subtract 400 from both sides:
480 - 400 = 400 * R * 4
80 = 1600 * R
Dividing both sides by 1600:
R = 80 / 1600
R = 0.05 or 5%
Now that we have determined the initial rate of interest, we can calculate the new rate of interest by increasing it by 2 percentage points.
New Rate of Interest = Initial Rate of Interest + Increase
New Rate of Interest = 5% + 2% = 7%
Finally, we can calculate the new amount by applying the new rate of interest to the initial sum.
New Amount = Principal (P) + (Principal (P) * New Rate of Interest * Time (T))
New Amount = 400 + (400 * 7% * 4)
New Amount = 400 + (400 * 0.07 * 4)
New Amount = 400 + 112
New Amount = ₹512
Therefore, the sum will amount to ₹512 if the rate of interest is increased by 2% per annum.