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) How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?
(2) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(3) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(5) How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 3 years.
(7) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 3 years.
(8) Ashley had to pay $5096 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?
(10) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 9% simple interest?