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) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.
(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?
(3) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?
(5) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?
(6) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(8) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(10) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.