Question

Sanju took a loan from the bank to buy a bike at the rate of 15 percent per annum compounded half yearly. He paid a C. I of rs 15507 after 1 1/2 years. Find his loan amount

Answer 1

half yearly
r= 15/2% half yearly
t= 1 1/2 years =( 18months/6 )=3time
a=p(1+r/100)t
a=p(1+15/200)^3
a=p(215/200)^3
a=p(43/40)^3

ci=a-p
15507=[p(43/40)^3]-p
15507=[p(79507/64000)-p]
15507=p(79507/64000-1)
15507=p×15507/64000
(15507×64000)/15507=p
64000=p

Answer 2

Answer:

The loan amount would be rs 64,000

Step-by-step explanation:

Let P be the amount of loan ( in rupees )

Annual rate = 15%,

⇒ Half yearly rate = 15/2%,

Compounding periods, t = 3 ( number of half years in 1 and 1/2 years )

Hence, the interest of compound interest,

$I=P(1+\frac{r}{100})^t-P$

$=P((1+\frac{15}{200})^{3}-1)$

$=P((1+\frac{3}{40})^{3}-1)$

$=P((\frac{43}{40})^{3}-1)$

According to the question,

$P((\frac{43}{40})^{3}-1) = 15507$

$P(\frac{79507}{64000}-1) = 15507$

$P(\frac{79507-64000}{64000})=15507$

$P(15507)=15507\times 64000$

$\implies P = 64000$

Learn more :

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