Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
Correct Answer
$7467.5
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 5%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 9
= $5150 ×5/100 × 9
= 5150 × 5 × 9/100
= 25750 × 9/100
= 231750/100
= $2317.5
Thus, Simple Interest = $2317.5
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 + $2317.5
= $7467.5
Thus, Amount to be paid = $7467.5 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) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 5% × 9)
= $5150 + ($5150 ×5/100 × 9)
= $5150 + (5150 × 5 × 9/100)
= $5150 + (25750 × 9/100)
= $5150 + (231750/100)
= $5150 + $2317.5 = $7467.5
Thus, Amount (A) to be paid = $7467.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5150, the simple interest in 1 year
= 5/100 × 5150
= 5 × 5150/100
= 25750/100 = $257.5
Thus, simple interest for 1 year = $257.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $257.5 × 9 = $2317.5
Thus, Simple Interest (SI) = $2317.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2317.5
= $7467.5
Thus, Amount to be paid = $7467.5 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(3) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.
(5) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 7 years.
(8) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.
(9) If John borrowed $3200 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?