Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.
Correct Answer
$8858
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 9%
Time (t) = 8 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% × 8
= $5150 ×9/100 × 8
= 5150 × 9 × 8/100
= 46350 × 8/100
= 370800/100
= $3708
Thus, Simple Interest = $3708
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 + $3708
= $8858
Thus, Amount to be paid = $8858 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) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 9% × 8)
= $5150 + ($5150 ×9/100 × 8)
= $5150 + (5150 × 9 × 8/100)
= $5150 + (46350 × 8/100)
= $5150 + (370800/100)
= $5150 + $3708 = $8858
Thus, Amount (A) to be paid = $8858 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 8 years
= Simple interest for 1 year × 8
= $463.5 × 8 = $3708
Thus, Simple Interest (SI) = $3708
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $3708
= $8858
Thus, Amount to be paid = $8858 Answer
Similar Questions
(1) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.
(3) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.
(4) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.
(6) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?
(8) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 8% simple interest?
(9) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(10) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.