Question

Calculate the amount and the compound interest by using formula (interest
compounded yearly).
• Principal = Rs 31,250, time =
2½
years, Rate = 12% p.a. (ans:41552 &10302 soln please)​

Answer 1

${\underline{\large{\pmb{\sf{Given...}}}}}$

★ The principal of Rs.31,250 is compounded of 2½ years annually at the rate of interest 12% per annum

${\underline{\large{\pmb{\sf{To \; Find...}}}}}$

★ The amount and the compound interest

${\underline{\large{\pmb{\sf{Understanding \; the \; concept...}}}}}$

☀️ Concept : Now, we have been given the principal amount which is 31,250 , the time which is 2½ and the rate of interest which is 12% per annum so, now let's use the formula which is to be used to find out the amount and later subtract it from the principal to find the compound interest

✰ Now here as we have been given the time in form of mixed fraction so, first let's find the amount for when compounded for 2 years and later use the simple interest formula and find the amount for the rest half year

${\underline{\large{\pmb{\sf{Using \; Concepts...}}}}}$

✪ Formula to find compound interest :

$\tt A = P\bigg[ 1 + \dfrac{r}{100} \bigg]^n$

✪ Formula to find simple interest :

$\tt S.I = \dfrac{p \times t \times r}{100}$

${\underline{\large{\pmb{\sf{Full \; Solution...}}}}}$

~ Now let's use the above mentioned formula and find out the amount for thee first 2 years

→ Formula

$:{\implies}\bf A = P \bigg[ 1 + \dfrac{r}{100} \bigg]^n$

→ Where,

• A stands for amount
• P stands for principal
• R stands for rate
• N stands for time

→ Here,

• Principal = 31250
• Rate = 12%
• Time = 2 years

~ Substituting the values we get,

➟ A = P [ 1 + r/100] ^n

➟ A = 31250 [1 + 12/100] ²

➟ A = 31250 [ 112/100 ] ²

➟ A = 31250 × 112/100 × 112/100

➟ A = 392000000/10000

➟ A = Rs.39200

• Henceforth amount is 39200 for 2 years

~ Now let's find the interest for the rest half year

→ Formula

${: \implies}\bf S.I = \dfrac{P \times T \times R}{100}$

→ Here,

• P stands for principal
• R stands for rate
• T stands for time

→ Where,

• Principal = 39200
• Rate = 12%
• Time 1/2 year

~ Substituting the values we get

➟ S.I = P × T × R / 100

➟  S.I = 39200 × 1/2 × 12 / 100

➟ S.I = 235200 / 100

➟ S.I = 2352

• Henceforth the interest for the rest half year is 2352

~ Now let's add up the result to find the amount for 2½

➟ Amount = 39200 + 2352

➟ Amount = 41552

• Henceforth the amount is 41552

~ Now in order to find the compound interest let's subtract the Principal from the Amount

➟ Compound Interest = A - P

➟ Compound Interest = 41552 - 31250

➟ Compound Interest = Rs.10302

• Henceforth the compound interest is 10302

${\underline{\large{\pmb{\sf{Additional \; Information...}}}}}$

• Formula to find the amount when compounded half yearly

$:{\implies}\bf A = P \bigg[ 1 + \dfrac{r}{200} \bigg]^{2n}$

• Formula to find the amount when compounded quarterly

${:\implies}\bf A = P \bigg[ 1 + \dfrac{r}{400} \bigg]^{4n}$

• Formula to find the amount when compounded at different rate of interests

${:\implies}\bf A = P \bigg[ 1 + \dfrac{r_2}{100} \bigg]\bigg[ 1 + \dfrac{r_2}{100} \bigg]\bigg[ 1 + \dfrac{r_3}{100} \bigg]$