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The simple interest on a certain sum of money for 2 years at 5% per annum is Rs 320. What will be the compound interest on the same sum for the same time at the same rate, the interest being calculated yearly? D 1800 cimple interest in 10 years. Find the The simple interest on a certain sum of money for 2 years at 5 % per annum is Rs 320. What will be the compound interest on the same sum for the same time at the same rate , the interest being calculated yearly ? D 1800 cimple interest in 10 years . Find the​

Sagot :

semsee45

Answer:

Rs 328

Step-by-step explanation:

Find the principal amount invested.

Simple Interest Formula

I = Prt

where:

  • I = interest earned
  • P = principal
  • r = interest rate (in decimal form)
  • t = time (in years)

Given:

  • I = Rs 320
  • r = 5% = 0.05
  • t = 2 years

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

⇒ 320 = P(0.05)(2)

⇒ 320 = P(0.1)

⇒ P = 3200

Compound Interest Formula

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

where:

  • I = interest earned
  • 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 = 3200
  • r = 5% = 0.05
  • n = 1 (annually)
  • t = 2 years

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

[tex]\implies \sf I=3200\left(1+\frac{0.05}{1}\right)^{2} -3200[/tex]

[tex]\implies \sf I=3200\left(1.05\right)^{2} -3200[/tex]

[tex]\implies \sf I=3200\left(1.1025\right) -3200[/tex]

[tex]\implies \sf I=3528-3200[/tex]

[tex]\implies \sf I=328[/tex]

Therefore, the compound interest on the same sum for the same time at the same rate is Rs 328.

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