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Mrs. S deposited Rs. $1, 00, 000$ in a nationalized bank for $3$ years. If the rate of interest is $7 %$ p.a., and interest is compounded annually. Calculate the amount at the end of third year (i.e., principal $+$ compound interest).

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Rs . 1, 22, 504.03

Rs . 1, 02, 504.30

Rs . 1, 22, 505.30

Rs . 1, 22, 405.30

answer is A.

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Detailed Solution

It is given that Rs. 1,00,000 was deposited for 3 years. Rate of interest is 7% p.a. and is compounded annually.
C.I. for 1 year is the same as SI.
So, C.I.

= \frac{P \times R \times T}{100}

Interest for the

1^{st}

year

= Rs . \frac{100000 \times 1 \times 7}{100}

\Rightarrow

Interest for the

1^{st}

year

= Rs . 7000

Amount after the

1^{st}

year

= Rs . 100000 + Rs . 7000

\Rightarrow

Amount after the

1^{st}

year

= Rs . 107000

Now this amount becomes principal for the second year.
Interest for the

2^{nd}

year

= Rs . \frac{107000 \times 1 \times 7}{100}

\Rightarrow

Interest for the

2^{nd}

year

= Rs . 7490

Amount after the

2^{nd}

year

= Rs . 107000 + Rs . 7490

\Rightarrow

Amount after the

2^{nd}

year

= Rs . 114490

Now this amount becomes principal for the third year.
Interest for the

3^{rd}

year

= Rs . \frac{114490 \times 1 \times 7}{100}

\Rightarrow

Interest for the

3^{rd}

year

= Rs . 8014.3

∴

Amount at the end of the

3^{rd}

year

= Rs . 114490 + Rs . 8014.3

\Rightarrow

Amount at the end of the

3^{rd}

year

= Rs . 122504.30

So, at the end of the third year the amount is Rs. 122504.30.
Hence, the correct option is 1.

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Mrs. S deposited Rs. 1,00,000 in a nationalized bank for 3years. If the rate of interest is 7% p.a., and interest is compounded annually. Calculate the amount at the end of third year (i.e., principal +compound interest).

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Mrs. S deposited Rs. $1, 00, 000$ in a nationalized bank for $3$ years. If the rate of interest is $7 %$ p.a., and interest is compounded annually. Calculate the amount at the end of third year (i.e., principal $+$ compound interest).