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) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.
(3) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(4) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?
(5) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?
(6) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 2% simple interest?
(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(9) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(10) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?