Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.
Correct Answer
$7139
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 3%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 7
= $5900 ×3/100 × 7
= 5900 × 3 × 7/100
= 17700 × 7/100
= 123900/100
= $1239
Thus, Simple Interest = $1239
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 + $1239
= $7139
Thus, Amount to be paid = $7139 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) = 3%
And, Time (t) = 7 years
Thus, Amount (A)
= $5900 + ($5900 × 3% × 7)
= $5900 + ($5900 ×3/100 × 7)
= $5900 + (5900 × 3 × 7/100)
= $5900 + (17700 × 7/100)
= $5900 + (123900/100)
= $5900 + $1239 = $7139
Thus, Amount (A) to be paid = $7139 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5900, the simple interest in 1 year
= 3/100 × 5900
= 3 × 5900/100
= 17700/100 = $177
Thus, simple interest for 1 year = $177
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $177 × 7 = $1239
Thus, Simple Interest (SI) = $1239
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $1239
= $7139
Thus, Amount to be paid = $7139 Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(2) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(3) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 5% simple interest?
(4) If Donald paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.
(6) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(7) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 9% simple interest?
(8) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?
(9) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) If Kimberly paid $5580 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.