Question

A sum of $40,000 is invested at a rate of 12 percent per year compounded annually. If
the investment is for a period of 5 years, what will the compound amount equal? How
much interest will be earned during the 5 years?​

Answer 1

Gɪᴠᴇɴ :-

• Principal = $40,000
• Rate = 12% per year compounded annually.
• Time = 5 Years.

Tᴏ Fɪɴᴅ :-

• How much Amount & interest will be earned during the 5 years ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

• when Rate is compounded annually :- Amount = Principal[ 1 + (Rate/100) ]^Time
• Compound interest = Amount - Principal.

Sᴏʟᴜᴛɪᴏɴ :-

Putting all values in formula , we get :-

➼ A = 40000[ 1 + (12/100)]⁵

➼ A = 40000[ 1 + (3/25)]⁵

➼ A = 40000*[28/25]⁵

➼ A = (40000*28*28*28*28*28)/(25*25*25*25*25)

➼ A ≈ $70493.67 (Ans).

And,

➺ CI = A - P

➺ CI = 70493.67 - 40000

➺ CI = $30493.67 (Ans.)

Hence, Amount gets After 5 Years is $70493.67 and interest gets is $30493.67 .

Answer 2

Answer:

• Principal = Rs. 40,000
• Rate = 12% p.c.p.a
• Time = 5 years

$\underline{\bigstar\:\textsf{Amount after compounded annually :}}$

$:\implies\sf Amount = P \times \bigg(1 +\dfrac{r}{100}\bigg)^{t}\\\\\\:\implies\sf Amount = 40000\times \bigg(1 +\dfrac{12}{100}\bigg)^{5}\\\\\\:\implies\sf Amount = 40000 \times \bigg(1 +\dfrac{3}{25}\bigg)^{5}\\\\\\:\implies\sf Amount = 40000\times \bigg(\dfrac{28}{25}\bigg)^{5}\\\\\\:\implies\sf Amount = 40000\times (1.12)^5\\\\\\:\implies\underline{\boxed{ \sf Amount = Rs.\:70493.67}}$

$\rule{150}{1}$

$\underline{\bigstar\:\textsf{Compound Interest Earned on Sum :}}$

$\dashrightarrow\sf\:\:CI=Amount- Principal\\\\\\\dashrightarrow\sf\:\:CI=Rs.\:70493.67-Rs.\:40000\\\\\\\dashrightarrow\:\:\underline{\boxed{\textsf{\textbf{CI = Rs. 30,493.67}}}}$

⠀

$\therefore\:\underline{\textsf{Compound Interest earned is \textbf{Rs. 30,493.67}.}}$