Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
Correct Answer
$9785
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5150 × 9% × 10
= $5150 ×9/100 × 10
= 5150 × 9 × 10/100
= 46350 × 10/100
= 463500/100
= $4635
Thus, Simple Interest = $4635
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $4635
= $9785
Thus, Amount to be paid = $9785 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5150
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 9% × 10)
= $5150 + ($5150 ×9/100 × 10)
= $5150 + (5150 × 9 × 10/100)
= $5150 + (46350 × 10/100)
= $5150 + (463500/100)
= $5150 + $4635 = $9785
Thus, Amount (A) to be paid = $9785 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5150, the simple interest in 1 year
= 9/100 × 5150
= 9 × 5150/100
= 46350/100 = $463.5
Thus, simple interest for 1 year = $463.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $463.5 × 10 = $4635
Thus, Simple Interest (SI) = $4635
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $4635
= $9785
Thus, Amount to be paid = $9785 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 3 years.
(4) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.
(6) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(8) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 7 years.
(10) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.