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).
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
3 answers
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
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
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
2 answers