Question:
Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
Correct Answer
$6985
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 3%
Time (t) = 9 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% × 9
= $5500 ×3/100 × 9
= 5500 × 3 × 9/100
= 16500 × 9/100
= 148500/100
= $1485
Thus, Simple Interest = $1485
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 + $1485
= $6985
Thus, Amount to be paid = $6985 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) = 9 years
Thus, Amount (A)
= $5500 + ($5500 × 3% × 9)
= $5500 + ($5500 ×3/100 × 9)
= $5500 + (5500 × 3 × 9/100)
= $5500 + (16500 × 9/100)
= $5500 + (148500/100)
= $5500 + $1485 = $6985
Thus, Amount (A) to be paid = $6985 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 9 years
= Simple interest for 1 year × 9
= $165 × 9 = $1485
Thus, Simple Interest (SI) = $1485
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $1485
= $6985
Thus, Amount to be paid = $6985 Answer
Similar Questions
(1) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 9% simple interest?
(2) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?
(3) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(4) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?
(6) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?
(7) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?
(8) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?
(9) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 3 years.