Question

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​

Answer 1

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

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

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:

$\implies \sf I=3200\left(1+\frac{0.05}{1}\right)^{2} -3200$

$\implies \sf I=3200\left(1.05\right)^{2} -3200$

$\implies \sf I=3200\left(1.1025\right) -3200$

$\implies \sf I=3528-3200$

$\implies \sf I=328$

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