Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
Correct Answer
$9180
Solution And Explanation
Solution
Given,
Principal (P) = $5100
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) = $5100 × 10% × 8
= $5100 ×10/100 × 8
= 5100 × 10 × 8/100
= 51000 × 8/100
= 408000/100
= $4080
Thus, Simple Interest = $4080
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 = $5100 + $4080
= $9180
Thus, Amount to be paid = $9180 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 = $5100
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5100 + ($5100 × 10% × 8)
= $5100 + ($5100 ×10/100 × 8)
= $5100 + (5100 × 10 × 8/100)
= $5100 + (51000 × 8/100)
= $5100 + (408000/100)
= $5100 + $4080 = $9180
Thus, Amount (A) to be paid = $9180 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 $5100, the simple interest in 1 year
= 10/100 × 5100
= 10 × 5100/100
= 51000/100 = $510
Thus, simple interest for 1 year = $510
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $510 × 8 = $4080
Thus, Simple Interest (SI) = $4080
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $4080
= $9180
Thus, Amount to be paid = $9180 Answer
Similar Questions
(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.
(2) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?
(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?
(4) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?
(5) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.
(6) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?
(7) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(8) If Jessica borrowed $3750 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?