Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.
Correct Answer
$7956
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5100 ×7/100 × 8
= 5100 × 7 × 8/100
= 35700 × 8/100
= 285600/100
= $2856
Thus, Simple Interest = $2856
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 + $2856
= $7956
Thus, Amount to be paid = $7956 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5100 + ($5100 × 7% × 8)
= $5100 + ($5100 ×7/100 × 8)
= $5100 + (5100 × 7 × 8/100)
= $5100 + (35700 × 8/100)
= $5100 + (285600/100)
= $5100 + $2856 = $7956
Thus, Amount (A) to be paid = $7956 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5100, the simple interest in 1 year
= 7/100 × 5100
= 7 × 5100/100
= 35700/100 = $357
Thus, simple interest for 1 year = $357
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $357 × 8 = $2856
Thus, Simple Interest (SI) = $2856
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $2856
= $7956
Thus, Amount to be paid = $7956 Answer
Similar Questions
(1) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?
(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 5% simple interest?
(4) If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.
(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?
(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.