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) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
(3) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 5% simple interest?
(4) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?
(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(7) Thomas had to pay $4370 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?
(9) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.
(10) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.