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Sagot :
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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