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) How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?
(2) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.
(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(5) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(6) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?
(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?
(9) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.