Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.
Correct Answer
$9204
Solution And Explanation
Solution
Given,
Principal (P) = $5900
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) = $5900 × 7% × 8
= $5900 ×7/100 × 8
= 5900 × 7 × 8/100
= 41300 × 8/100
= 330400/100
= $3304
Thus, Simple Interest = $3304
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 = $5900 + $3304
= $9204
Thus, Amount to be paid = $9204 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 = $5900
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5900 + ($5900 × 7% × 8)
= $5900 + ($5900 ×7/100 × 8)
= $5900 + (5900 × 7 × 8/100)
= $5900 + (41300 × 8/100)
= $5900 + (330400/100)
= $5900 + $3304 = $9204
Thus, Amount (A) to be paid = $9204 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 $5900, the simple interest in 1 year
= 7/100 × 5900
= 7 × 5900/100
= 41300/100 = $413
Thus, simple interest for 1 year = $413
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $413 × 8 = $3304
Thus, Simple Interest (SI) = $3304
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $3304
= $9204
Thus, Amount to be paid = $9204 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 4 years.
(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.
(5) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.
(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?
(9) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?
(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?