Question:
Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
Correct Answer
$7150
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 3%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 10
= $5500 ×3/100 × 10
= 5500 × 3 × 10/100
= 16500 × 10/100
= 165000/100
= $1650
Thus, Simple Interest = $1650
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 + $1650
= $7150
Thus, Amount to be paid = $7150 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) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5500 + ($5500 × 3% × 10)
= $5500 + ($5500 ×3/100 × 10)
= $5500 + (5500 × 3 × 10/100)
= $5500 + (16500 × 10/100)
= $5500 + (165000/100)
= $5500 + $1650 = $7150
Thus, Amount (A) to be paid = $7150 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5500, the simple interest in 1 year
= 3/100 × 5500
= 3 × 5500/100
= 16500/100 = $165
Thus, simple interest for 1 year = $165
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $165 × 10 = $1650
Thus, Simple Interest (SI) = $1650
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $1650
= $7150
Thus, Amount to be paid = $7150 Answer
Similar Questions
(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?
(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) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(5) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.
(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?
(7) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 4 years.
(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.