Find the amount and the compound interest on 15000 for 3 years at 10% per annum compounded annually

Find the amount and compounded interest on Rs.15000 in 2`(1)/(2)` years at 10% p.a. compounded annually.

Here P = Rs.15000, t = 2`(1)/(2)`, r = 10%
Now, Amount after 2 year
= `"P"(1 + "r"/100)^"t"`

= `15000(1 + 10/100)^2`

= `15000(11/10)^2`
= 18150
Now interest for the next half year
= `(18150 xx 10)/(100 xx 2)`
= 907.5
Hence, Amount
= Rs.18150 + Rs.907.50
= Rs.19057.50
Also, C.I.
= A - P
= Rs.19057.50 - Rs.15000
= Rs.4057.50.

Concept: Concept of Compound Interest - When the Time is Not an Exact Number of Years and the Interest is Compounded Yearly

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Calculate the amount, if ₹15,000 is lent at compound interest for 2 years and the rates for the successive years at 8% p.a. and 10% p.a. respectively.

Answer

Verified

Hint: Amount yielded from the first year as in simple interest becomes principal sum for the second year when
rate is compounded annually.

Formula used:
$A = P\left( {1 + \dfrac{{{R_1}}}{{100}}} \right)\left( {1 + \dfrac{{{R_2}}}{{100}}} \right)$

Complete step-by-step answer:
Where A – compound amount
P – Principal sum
$R_1$ – rate of interest for first year
$R_2$ – rate of interest for second year
Here, we are given P = ₹15000
$R_1$ = 8 % P.a
$R_2$ = 10% P.a.
Here we will put the values of P, R 1 , R 2 and T in the formula of amount.
Therefore, \[A = 15000\left( {1 + \dfrac{8}{{100}}} \right)\left( {1 + \dfrac{{10}}{{100}}} \right)\]
\[ = 15000 \times \dfrac{{108}}{{100}} \times \dfrac{{110}}{{100}}\]=
= ₹17820.
Thus, the compound amount is ₹17820.

Note: Please note that here the interest is compounded. So, this means to say that we have to apply the formula of compound interest and not that of simple interest.

Solution

For 1st year Principal (P)=Rs. 15000, Rate (R)=6% Time (T)=1 year (adsbygoogle = window.adsbygoogle || []).push({}); ∴ Interest =P×R×T100=15000×6×1100=150×6=Rs.900 ∴ Amount at the end of 1st year=Rs. 15000+Rs. 900=Rs.15900 For 2nd yearP=Rs. 15900,R=8%,T=1 year ∴ Interest =15900×8×1100=159×8=Rs.1272 ∴ Amount at the end of 2nd year=Rs. (15900+1272)=Rs. 17172 [∵ Amount =P+I] For 3rd year (adsbygoogle = window.adsbygoogle || []).push({}); P=Rs.17172,R=10%,T=1 year ∴ Interest =17172×10×1100=Rs.1717.20 ∴ Amount at the end of 3rd year=Rs. (17172+1717.20)=Rs. 18889.20 ∴ Compound interest =18889.20−15000=Rs.3889.20

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