Question:
Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.
Correct Answer
$7450
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 7%
Time (t) = 7 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) = $5000 × 7% × 7
= $5000 ×7/100 × 7
= 5000 × 7 × 7/100
= 35000 × 7/100
= 245000/100
= $2450
Thus, Simple Interest = $2450
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 = $5000 + $2450
= $7450
Thus, Amount to be paid = $7450 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 = $5000
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5000 + ($5000 × 7% × 7)
= $5000 + ($5000 ×7/100 × 7)
= $5000 + (5000 × 7 × 7/100)
= $5000 + (35000 × 7/100)
= $5000 + (245000/100)
= $5000 + $2450 = $7450
Thus, Amount (A) to be paid = $7450 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 $5000, the simple interest in 1 year
= 7/100 × 5000
= 7 × 5000/100
= 35000/100 = $350
Thus, simple interest for 1 year = $350
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $350 × 7 = $2450
Thus, Simple Interest (SI) = $2450
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $2450
= $7450
Thus, Amount to be paid = $7450 Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.
(2) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.
(3) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(4) If Thomas paid $4408 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) How much loan did Charles borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6490 to clear it?
(6) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?
(8) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(9) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.
(10) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?