Question

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​

Answer 1

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.

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