Answered

Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

How much will a sum of ¥4000 amount to in 1 1/2 yrs at 10% per annum compound interest,interest being paid half-yearly​

Sagot :

semsee45

Answer:

¥4630.50

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}[/tex]

where:

  • A = final amount
  • P = principal amount
  • r = interest rate (in decimal form)
  • n = number of times interest applied per time period
  • t = number of time periods elapsed

Given:

  • P = 4000
  • r = 10% = 0.1
  • n = 2
  • t = 1.5

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=4000\left(1+\dfrac{0.1}{2}\right)^{2 \times 1.5}[/tex]

[tex]\implies \sf A=4000\left(1.05\right)^{3}[/tex]

[tex]\implies \sf A=4630.50[/tex]

Itz5151

Answer:

¥4630.50

Step-by-step explanation:

Here,

  • P = ¥4000
  • n = 1 1/2 = 3/2 years
  • r = 10% per annum

ATQ, as well,the interest is payable in half-yearly.

We know that,

  • [By this formula,it could easily solved]

[tex] \boxed{\rm \: A = P \bigg(1+ \cfrac{ \cfrac{r}{2} }{100} \bigg) {}^{2n} }[/tex]

Substitute the values

[tex]A = 4000 \bigg(1 + \cfrac{5}{100} \bigg) {}^{2 \times \frac{3}{2} } [/tex]

Now solve.

[tex]A = 4000 * (21/20)^3[/tex]

[tex] \implies \: A = 4000 \times \cfrac{21}{20} \times \cfrac{21}{20} \times \cfrac{21}{20} = \cfrac{21 \times 21 \times 21}{2} [/tex]

[tex] \implies \: A = \: \yen \: 4630.50[/tex]

Hence,the sum of ¥ 4000 will be amounted to ¥4630.50 in 1 1/2 years.

[tex] \rule{225pt}{2pt}[/tex]

This question arises:Why we used that formula?

Reason:

The compound interest is calculated half-yearly, the formula changes a little.In this case for r we write r/2 and for n we write 2n because a rate of r% per annum is r/2% half-yearly and n years = 2n half year So this is the reason.

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.