Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
Correct Answer
$9270
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5150 ×10/100 × 8
= 5150 × 10 × 8/100
= 51500 × 8/100
= 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 10% × 8)
= $5150 + ($5150 ×10/100 × 8)
= $5150 + (5150 × 10 × 8/100)
= $5150 + (51500 × 8/100)
= $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 = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5150, the simple interest in 1 year
= 10/100 × 5150
= 10 × 5150/100
= 51500/100 = $515
Thus, simple interest for 1 year = $515
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $515 × 8 = $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) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
(3) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?
(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.
(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(7) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.
(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 7% simple interest?