Question:
Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
Correct Answer
$8250
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 5%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5500 × 5% × 10
= $5500 ×5/100 × 10
= 5500 × 5 × 10/100
= 27500 × 10/100
= 275000/100
= $2750
Thus, Simple Interest = $2750
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 = $5500 + $2750
= $8250
Thus, Amount to be paid = $8250 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 = $5500
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5500 + ($5500 × 5% × 10)
= $5500 + ($5500 ×5/100 × 10)
= $5500 + (5500 × 5 × 10/100)
= $5500 + (27500 × 10/100)
= $5500 + (275000/100)
= $5500 + $2750 = $8250
Thus, Amount (A) to be paid = $8250 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5500, the simple interest in 1 year
= 5/100 × 5500
= 5 × 5500/100
= 27500/100 = $275
Thus, simple interest for 1 year = $275
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $275 × 10 = $2750
Thus, Simple Interest (SI) = $2750
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $2750
= $8250
Thus, Amount to be paid = $8250 Answer
Similar Questions
(1) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
(2) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(3) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(4) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.
(7) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.
(8) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(10) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.