Q1)The length of time for $5000 to earn $1000 if invested at 10% per annum
AND
Q2)Khalid invests $6750 at 8.5% per annum.How much interest has he earned and what is the total amount in his account after 4 years?
Umm thanks in advance and also pls show all the steps even the minor steps in great details thanks 😊
Q1)principle:$5000
Rate : 10%
S.I = $1000
Therefore length of time =
S.I x 100 divided by Principle x rate
=1000x100 divided by 5000 x 10
Answer=2years.
Q2) principle:$6750
Rate:8.5%
Time:4 years
Simple interest=
PRT/100
Therefore S.I =
6750*85*4/1000=$2295
Amount=S.I+ Principle
Therefore amount=$2295+$6750=$9045
Answers:S.I:$2295,amount:$9045.
Thanks
Thank you kind bro or girl
Q1) Well, well, well, let's calculate the time it takes for $5000 to earn $1000 at a dazzling 10% per year!
To do this, we need to use a magical formula called the compound interest formula: A = P(1 + r/n)^(nt), where:
A is the future amount we want - in this case, $6000 (our initial amount of $5000 plus the $1000 interest we want),
P is the principal amount - in this case, $5000,
r is the annual interest rate - 10% (we convert it to a decimal, so 0.10),
n is the number of times the interest is compounded per year - let's assume yearly compounding (n = 1),
and t is the time in years we're trying to find out.
Now let's solve for t:
A = P(1 + r/n)^(nt)
6000 = 5000(1 + 0.10/1)^(1t)
To simplify:
1.2 = (1.10)^t
Now, to get rid of that pesky exponent, we need to use our clown math skills and take the log base 1.10 of 1.2 (or use logarithmic functions on a calculator).
t ≈ log(1.2) / log(1.10)
*takes out a calculator and starts doing clown math*
*tap tap tap*
*takes a pie break*
After some rigorous clown calculations, we find that t is approximately 7.27 years! So, it would take around 7.27 years for $5000 to earn $1000 with a 10% interest rate.
Q2) Oh, Khalid is getting into the investment game too? How exciting! Let's see how much he has earned and the total amount in his account after 4 years.
To calculate the interest earned, we'll use the simple interest formula: I = P * r * t, where:
I is the interest earned,
P is the principal amount - $6750 here,
r is the annual interest rate - 8.5% (again, converted to decimal, so 0.085),
and t is the time - 4 years.
Now, let's calculate the interest:
I = 6750 * 0.085 * 4
Clown math time!
Calculating...
*taking a juggling break*
Oh, Khalid has earned $2310 in interest! Great job, Khalid!
Now let's find the total amount in his account after 4 years, including the interest. We'll just add the interest to the principal amount, like a clown mixing colors!
Total amount = Principal + Interest
Total amount = 6750 + 2310
More clown math!
Calculating...
After adding and juggling numbers around, the total amount in Khalid's account after 4 years is $9060.
There you have it! Khalid has earned $2310 in interest and now has a total amount of $9060 in his investment account. Keep it up, Khalid!
Rupashi, the formula is PxRxT/100.....so why have you put 1000 insted of 100????
Sure! I'm here to help. Let's work on the questions step by step.
Q1) The length of time for $5000 to earn $1000 if invested at 10% per annum:
To find the length of time, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, we are given:
P = $5000
A = P + $1000 = $6000 (since the interest earned is $1000 and we add it to the initial principal)
r = 10% per annum = 0.10
n = 1 (interest is compounded annually)
Now, we can substitute the given values into the formula and solve for t:
$6000 = $5000(1 + 0.10/1)^(1*t)
To simplify, let's divide both sides by $5000:
1.2 = (1.10)^t
To solve for t, we need to take the logarithm of both sides. Let's use the natural logarithm (ln) for this example:
ln(1.2) = ln(1.10)^t
Now, we can bring down the exponent using the logarithm property:
ln(1.2) = t * ln(1.10)
Now, divide both sides by ln(1.10) to isolate t:
t = ln(1.2) / ln(1.10)
Calculating the right side of the equation:
t = 0.182322 / 0.0953102
t ≈ 1.913 years
Therefore, it would take approximately 1.913 years for $5000 to earn $1000 at an interest rate of 10% per annum.
Q2) Khalid invests $6750 at 8.5% per annum. How much interest has he earned, and what is the total amount in his account after 4 years:
To calculate the interest earned, we can use the simple interest formula:
Interest = Principal x Rate x Time
In this case, we are given:
Principal = $6750
Rate = 8.5% per annum = 0.085
Time = 4 years
Now, we can substitute the values into the formula:
Interest = $6750 x 0.085 x 4
Calculating the right side of the equation:
Interest = $2310
Therefore, Khalid has earned $2310 in interest.
To find the total amount in his account after 4 years, we can use the formula:
Total Amount = Principal + Interest
Total Amount = $6750 + $2310
Calculating the right side of the equation:
Total Amount = $9060
Therefore, there will be a total of $9060 in Khalid's account after 4 years, including the interest earned.