Question

find a compound amount of rs 850000 for 20 years that pays at the rate of 12 % per annum. compounded monthly​

Answer 1

Answer:

Compound amount will be Rs 92,58,670.61

Step-by-step explanation:

Given :

Principal = Rs 8,50,000

Time = 20 Years

Interest rate = 12 % per annum Compounded Monthly

To Find :

Compound Amount

Solution :

A = Compound amount ( Future value of investment)

P = The principal amount (The initial deposit or loan amount)

r = Interest rate per annum

n = Time

$\rule{300}{1.5}$

★ According to the Question :

A = P $\sf{(1+\dfrac{r}{100})^{(n \times 12)}}$

⇒ A = 8,50,000$\sf{(1 + \dfrac{\left(\frac{12}{12}\right)}{100})^{(20 \times 12)}}$

⇒ A = $\sf{8,50,000(1 + 0.01) ^{(240)}}$

⇒ A = $\sf{8,50,000 \times 10.892553}$

⇒ A = $\sf{92,58,670.61}$

$\rule{300}{1.5}$

• Principal Amount = Rs 8,50,000

• Total Interest = Rs 8,408,670.61

• Compound amount = Rs 92,58,670.61

Therefore,

Compound amount will be Rs 92,58,670.61

Answer 2

$\underline{\underline{\textsf{\maltese\:\: Given :}}}$

☞ Principal (P) = Rs 850000

☞ Time (T) = 20 years

☞ Rate % (R) = 12% per annum compounded monthly

$\underline{\underline{\textsf{\maltese\:\: To Find :}}}$

☞ Compound Amount = ?

$\underline{\underline{\textsf{\maltese\:\: Concept Implemented :}}}$

$\displaystyle \bf A = P\left(1 + \frac{r}{n\, * \, 100}\right)^{nt}$

Where,

➢ A = Amount

➢ P = Principal

➢ r = Rate of interest

➢ n = Number of times interest applied per time period.

• For annually n = 1

• For semi annually n = 2

• For monthly n = 12

• For weekly n = 52

• For daily n = 365

➢ t = Time

$\underline{\underline{\textsf{\maltese\:\: Solution:}}}$

$\displaystyle \bf A = P\left(1 + \frac{r}{n\, * \, 100}\right)^{nt}$

Here ,

P = Rs 850000

r = 12%

n = 12

t = 20 years

$\displaystyle \bf A = P\left(1 + \frac{r}{n\, * \, 100}\right)^{nt}$

$\displaystyle \sf A = P \left( 1 + \frac{12}{12 \, * \, 100}\right)^{12 \,* \, 20}$

$\displaystyle \sf A = 850000\left(1 + \frac{1}{100}\right)^{240}$

$\displaystyle \sf A =850000(1 + 0.01)^{240}$

$\displaystyle \sf A = 850000(1.01)^{240}$

$\displaystyle \sf A = 850000 \; * \; 10.892553$

$\displaystyle \sf A = R_s \, 9258670.61$

∴ Compound Amount = Rs 9258670.61