Question:
What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?
Correct Answer
$4725
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 7%
Time (t) = 5 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) = $3500 × 7% × 5
= $3500 ×7/100 × 5
= 3500 × 7 × 5/100
= 24500 × 5/100
= 122500/100
= $1225
Thus, Simple Interest = $1225
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 = $3500 + $1225
= $4725
Thus, Amount to be paid = $4725 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 = $3500
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 5 years
Thus, Amount (A)
= $3500 + ($3500 × 7% × 5)
= $3500 + ($3500 ×7/100 × 5)
= $3500 + (3500 × 7 × 5/100)
= $3500 + (24500 × 5/100)
= $3500 + (122500/100)
= $3500 + $1225 = $4725
Thus, Amount (A) to be paid = $4725 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 $3500, the simple interest in 1 year
= 7/100 × 3500
= 7 × 3500/100
= 24500/100 = $245
Thus, simple interest for 1 year = $245
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $245 × 5 = $1225
Thus, Simple Interest (SI) = $1225
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $1225
= $4725
Thus, Amount to be paid = $4725 Answer
Similar Questions
(1) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(3) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?
(4) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(6) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(8) William had to pay $3920 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.