Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
Correct Answer
$9270
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 8%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 10
= $5150 ×8/100 × 10
= 5150 × 8 × 10/100
= 41200 × 10/100
= 412000/100
= $4120
Thus, Simple Interest = $4120
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 + $4120
= $9270
Thus, Amount to be paid = $9270 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) = 8%
And, Time (t) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 8% × 10)
= $5150 + ($5150 ×8/100 × 10)
= $5150 + (5150 × 8 × 10/100)
= $5150 + (41200 × 10/100)
= $5150 + (412000/100)
= $5150 + $4120 = $9270
Thus, Amount (A) to be paid = $9270 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5150, the simple interest in 1 year
= 8/100 × 5150
= 8 × 5150/100
= 41200/100 = $412
Thus, simple interest for 1 year = $412
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $412 × 10 = $4120
Thus, Simple Interest (SI) = $4120
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $4120
= $9270
Thus, Amount to be paid = $9270 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.
(2) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.
(5) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(6) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?
(7) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.
(8) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?
(9) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.