sum of money borrowed at a particular rate of interest amounts of Rs 8320 in 2years and Rs 9685 in 3 and half years.Find the sum borrowed
I interpret the question as:
Given:
1. future value (i.e. amount owing at maturity) of a two-year loan is Rs 8329 and that of
2. future value of a three-year loan is Rs 9685.
Find the sum of the present value of the loans.
P1=8320/(1+i)^2
P2=9685/(1+i)^3.5
sum=P1+P2
where i is the EAR (effective annual rate).
Interest for 1 year = Rs. 9685-8320 = 1365
Interest for 2 years= Rs 1365*2 = 2730
since the total amount after 2 years is Rs. 8320
so, borrowed money = Rs. 8320 - 2730 = Rs.5590
Guess I misread the question. There was only one sum borrowed at an unknown rate of interest i,
assumed compound interest compounded annually for 2 and 3.5 years respectively.
Let
P=sum borrowed
i=interest rate
P(1+i)^2=8320
P(1+i)^(3.5)=9685
=>
9685/8320=P(1+i)^(3.5-2)=(1+i)^1.5
=>
(1+i)=(9685/8320)^(2/3)=1.106584, or
i=0.106584
P(1+i)²=8320
=>
P=8320/(1+i)²
=8320/(1.106584²)
=Rs 7158.64
To find the sum borrowed, we can set up a system of equations based on the given information.
Let's assume that the sum borrowed is denoted by 'P' and the rate of interest is denoted by 'r'.
We are given two situations:
1. After 2 years, the sum of money amounts to Rs 8320.
2. After 3.5 years, the sum of money amounts to Rs 9685.
Using the formula for compound interest, the amount after 2 years can be calculated as:
Amount1 = P * (1 + r/100)^2 = Rs 8320
Similarly, the amount after 3.5 years can be calculated as:
Amount2 = P * (1 + r/100)^3.5 = Rs 9685
Now, we have a system of two equations:
Equation 1: P * (1 + r/100)^2 = 8320
Equation 2: P * (1 + r/100)^3.5 = 9685
To solve this system of equations, we can use the substitution method or elimination method.
Let's use the substitution method:
From Equation 1, we can express P in terms of r: P = 8320 / (1 + r/100)^2
Now, substitute this value of P in Equation 2:
(8320 / (1 + r/100)^2) * (1 + r/100)^3.5 = 9685
Simplify the equation:
8320 * (1 + r/100)^1.5 = 9685
Divide both sides by 8320:
(1 + r/100)^1.5 = 9685 / 8320
Take the square root of both sides:
1 + r/100 = √(9685 / 8320)
Subtract 1 from both sides:
r/100 = √(9685 / 8320) - 1
Multiply by 100 on both sides:
r = (100 * (√(9685 / 8320) - 1))
Now that we have the value of r, we can substitute it back into Equation 1 to find P:
P = 8320 / (1 + (100 * (√(9685 / 8320) - 1))/100)^2
Simplify the equation to find the value of P, which represents the sum borrowed.
It is important to note that the above calculations are based on the assumption that the interest is compounded annually. If the compounding period is different, the formula and calculations may vary.