Question:
Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
Correct Answer
$8500
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 7%
Time (t) = 10 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% × 10
= $5000 ×7/100 × 10
= 5000 × 7 × 10/100
= 35000 × 10/100
= 350000/100
= $3500
Thus, Simple Interest = $3500
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 + $3500
= $8500
Thus, Amount to be paid = $8500 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) = 10 years
Thus, Amount (A)
= $5000 + ($5000 × 7% × 10)
= $5000 + ($5000 ×7/100 × 10)
= $5000 + (5000 × 7 × 10/100)
= $5000 + (35000 × 10/100)
= $5000 + (350000/100)
= $5000 + $3500 = $8500
Thus, Amount (A) to be paid = $8500 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 10 years
= Simple interest for 1 year × 10
= $350 × 10 = $3500
Thus, Simple Interest (SI) = $3500
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $3500
= $8500
Thus, Amount to be paid = $8500 Answer
Similar Questions
(1) If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?
(3) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.
(5) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.
(8) Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 8% simple interest?