Neeraj lent 65536 for 2 years at 12% per annum, compounded annually. How much
more could he earn if the interest were compounded half-yearly?
Sudershan denosited 32000 in a bank, where the interest is credited quarterly. If the rate
Answers
Formula used: A=P(1+rn)ntA=P(1+rn)nt
Where A= Final amount
P = Initial principal balance
r = Rate of interest
n= number of times interest applied per time period
t = number of time periods elapsed
Complete step-by-step answer:
It is given that Neeraj lent Rs.65536 for 2 years at 1212%=252%1212%=252% per annum, compounded annually.
So the total amount Neeraj get after 2 years compounded annually is given by the formula given in the hint
Here P=65536, n=1, r=252%,t=2P=65536, n=1, r=252%,t=2
By substituting the values we get, A=65536×⎛⎝⎜⎜1+2521001⎞⎠⎟⎟1×2A=65536×(1+2521001)1×2
On further solving we get,
A=65536×(1+25200)2A=65536×(1+25200)2
Which in turn imply that,
A=65536×(1+18)2A=65536×(1+18)2
That is
A=65536×98×98A=65536×98×98
A=82944A=82944
The interest amount is found by subtracting the principal amount from the total amount.
Thus the interest amount is Rs. (82944 – 65536) = Rs.17408.
Now the total amount Neeraj get after 2 years compounded half-yearly is found,
HereP=65536, n=2, r=252%,t=2P=65536, n=2, r=252%,t=2
Since it is compounded half – yearly here we take n=2n=2
A=65536×⎛⎝⎜⎜1+2521001⎞⎠⎟⎟2×2A=65536×(1+2521001)2×2
On solving the above equation,
A=65536×(1+25400)4A=65536×(1+25400)4
A=65536×(1+116)4A=65536×(1+116)4
Let us solve further we get,
A=65536×1716×1716×1716×1716A=65536×1716×1716×1716×1716
A=83521A=83521
The interest amount is found by subtracting the principal amount from the total amount.
Thus the interest amount is Rs. (83521 – 65536) = Rs.17985.
Hence Neeraj could earn Rs. (17985 – 17408)=Rs. 577 if the interest were compounded half-yearly instead of annually.