QuestionDeposit $\$ P$ for 2 years at $8\%$ p.a. Find interest for (i) simple interest and (ii) compound interest. If difference is $\$ 240$ , find $P$ .

Studdy Solution

STEP 1

Assumptions1. The principal amount is $$ . The interest rate is8% per annum3. The time for the deposit is years4. The interest is calculated using simple interest and compounded yearly5. The difference between the simple interest and compound interest is $240

STEP 2

First, we need to express the simple interest in terms of $. The formula for simple interest is$ Interest = Principal\, amount \\times Interest\, rate \\times Time$$

STEP 3

Now, plug in the given values for the principal amount, interest rate, and time to express the simple interest in terms of $$.
$Interest = \\times8\% \\times2\, years$

STEP 4

Convert the percentage to a decimal value.
$8\% =0.08$ $Interest = \\times0.08 \\times2\, years$

STEP 5

Calculate the simple interest in terms of $$.
$Interest = \\times0.08 \\times2\, years =0.16$

STEP 6

Next, we need to express the compound interest in terms of $. The formula for compound interest is$ Interest = Principal\, amount \\times (1 + Interest\, rate)^{Time} - Principal\, amount$$

STEP 7

Now, plug in the given values for the principal amount, interest rate, and time to express the compound interest in terms of $$.
$Interest = \\times (1 +\%)^{2\, years} -$

STEP 8

Convert the percentage to a decimal value.
$8\% =0.08$ $Interest = \\times (1 +0.08)^{2\, years} -$

STEP 9

Calculate the compound interest in terms of $$.
$Interest = \\times (.08)^{2\, years} - =(.1664 -) =.1664$

STEP 10

The difference between the simple interest and the compound interest is given as $240. So, we can set up the following equation$ $0.1664 -0.16 =240$ $

STEP 11

implify the equation to find the value of $$.
$0.0064 =240$

STEP 12

olve for $$.
$=240 /0.0064 = \$37500$ The value of $$ is $37500.

Was this helpful?

QuestionDeposit $\$ P$ for 2 years at $8\%$ p.a. Find interest for (i) simple interest and (ii) compound interest. If difference is $\$ 240$ , find $P$ .

Studdy Solution

STEP 1

Assumptions1. The principal amount is $$ . The interest rate is8% per annum3. The time for the deposit is years4. The interest is calculated using simple interest and compounded yearly5. The difference between the simple interest and compound interest is $240

STEP 2

First, we need to express the simple interest in terms of $. The formula for simple interest is$ Interest = Principal\, amount \\times Interest\, rate \\times Time$$

STEP 3

Now, plug in the given values for the principal amount, interest rate, and time to express the simple interest in terms of $$.
$Interest = \\times8\% \\times2\, years$

STEP 4

Convert the percentage to a decimal value.
$8\% =0.08$ $Interest = \\times0.08 \\times2\, years$

STEP 5

Calculate the simple interest in terms of $$.
$Interest = \\times0.08 \\times2\, years =0.16$

STEP 6

Next, we need to express the compound interest in terms of $. The formula for compound interest is$ Interest = Principal\, amount \\times (1 + Interest\, rate)^{Time} - Principal\, amount$$

STEP 7

Now, plug in the given values for the principal amount, interest rate, and time to express the compound interest in terms of $$.
$Interest = \\times (1 +\%)^{2\, years} -$

STEP 8

Convert the percentage to a decimal value.
$8\% =0.08$ $Interest = \\times (1 +0.08)^{2\, years} -$

STEP 9

Calculate the compound interest in terms of $$.
$Interest = \\times (.08)^{2\, years} - =(.1664 -) =.1664$

STEP 10

The difference between the simple interest and the compound interest is given as $240. So, we can set up the following equation$ $0.1664 -0.16 =240$ $

STEP 11

implify the equation to find the value of $$.
$0.0064 =240$

STEP 12

olve for $$.
$=240 /0.0064 = \$37500$ The value of $$ is $37500.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionDeposit $P\$ P$P for 2 years at 8%8\%8% p.a. Find interest for (i) simple interest and (ii) compound interest. If difference is $240\$ 240$240, find PPP.

Studdy Solution

STEP 1

Assumptions1. The principal amount is $$ . The interest rate is8% per annum3. The time for the deposit is years4. The interest is calculated using simple interest and compounded yearly5. The difference between the simple interest and compound interest is $240

STEP 2

First, we need to express the simple interest in terms of .Theformulaforsimpleinterestis. The formula for simple interest is.TheformulaforsimpleinterestisInterest = Principal\, amount \\times Interest\, rate \\times Time$$

STEP 3

Now, plug in the given values for the principal amount, interest rate, and time to express the simple interest in terms of $$.Interest=times8%times2 yearsInterest = \\times8\% \\times2\, yearsInterest=times8%times2years

STEP 4

Convert the percentage to a decimal value.8%=0.088\% =0.088%=0.08Interest=times0.08times2 yearsInterest = \\times0.08 \\times2\, yearsInterest=times0.08times2years

STEP 5

Calculate the simple interest in terms of $$.Interest=times0.08times2 years=0.16Interest = \\times0.08 \\times2\, years =0.16Interest=times0.08times2years=0.16

STEP 6

Next, we need to express the compound interest in terms of .Theformulaforcompoundinterestis. The formula for compound interest is.TheformulaforcompoundinterestisInterest = Principal\, amount \\times (1 + Interest\, rate)^{Time} - Principal\, amount$$

STEP 7

Now, plug in the given values for the principal amount, interest rate, and time to express the compound interest in terms of $$.Interest=times(1+%)2 years−Interest = \\times (1 +\%)^{2\, years} -Interest=times(1+%)2years−

STEP 8

Convert the percentage to a decimal value.8%=0.088\% =0.088%=0.08Interest=times(1+0.08)2 years−Interest = \\times (1 +0.08)^{2\, years} -Interest=times(1+0.08)2years−

STEP 9

Calculate the compound interest in terms of $$.Interest=times(.08)2 years−=(.1664−)=.1664Interest = \\times (.08)^{2\, years} - =(.1664 -) =.1664Interest=times(.08)2years−=(.1664−)=.1664

STEP 10

The difference between the simple interest and the compound interest is given as 240.So,wecansetupthefollowingequation240. So, we can set up the following equation240.So,wecansetupthefollowingequation0.1664−0.16=2400.1664 -0.16 =2400.1664−0.16=240$

STEP 11

implify the equation to find the value of $$.0.0064=2400.0064 =2400.0064=240

STEP 12

olve for $$.=240/0.0064=$37500 =240 /0.0064 = \$37500=240/0.0064=$37500The value of $$ is $37500.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionDeposit $\$ P$ for 2 years at $8\%$ p.a. Find interest for (i) simple interest and (ii) compound interest. If difference is $\$ 240$ , find $P$ .

First, we need to express the simple interest in terms of $. The formula for simple interest is$ Interest = Principal\, amount \\times Interest\, rate \\times Time$$

Now, plug in the given values for the principal amount, interest rate, and time to express the simple interest in terms of $$.
$Interest = \\times8\% \\times2\, years$

Convert the percentage to a decimal value.
$8\% =0.08$ $Interest = \\times0.08 \\times2\, years$

Calculate the simple interest in terms of $$.
$Interest = \\times0.08 \\times2\, years =0.16$

Next, we need to express the compound interest in terms of $. The formula for compound interest is$ Interest = Principal\, amount \\times (1 + Interest\, rate)^{Time} - Principal\, amount$$

Now, plug in the given values for the principal amount, interest rate, and time to express the compound interest in terms of $$.
$Interest = \\times (1 +\%)^{2\, years} -$

Convert the percentage to a decimal value.
$8\% =0.08$ $Interest = \\times (1 +0.08)^{2\, years} -$

Calculate the compound interest in terms of $$.
$Interest = \\times (.08)^{2\, years} - =(.1664 -) =.1664$

The difference between the simple interest and the compound interest is given as $240. So, we can set up the following equation$ $0.1664 -0.16 =240$ $

implify the equation to find the value of $$.
$0.0064 =240$

olve for $$.
$=240 /0.0064 = \$37500$ The value of $$ is $37500.