Question:
Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.
Correct Answer
$7175.5
Solution And Explanation
Solution
Given,
Principal (P) = $5650
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) = $5650 × 3% × 9
= $5650 ×3/100 × 9
= 5650 × 3 × 9/100
= 16950 × 9/100
= 152550/100
= $1525.5
Thus, Simple Interest = $1525.5
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 = $5650 + $1525.5
= $7175.5
Thus, Amount to be paid = $7175.5 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 = $5650
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5650 + ($5650 × 3% × 9)
= $5650 + ($5650 ×3/100 × 9)
= $5650 + (5650 × 3 × 9/100)
= $5650 + (16950 × 9/100)
= $5650 + (152550/100)
= $5650 + $1525.5 = $7175.5
Thus, Amount (A) to be paid = $7175.5 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 $5650, the simple interest in 1 year
= 3/100 × 5650
= 3 × 5650/100
= 16950/100 = $169.5
Thus, simple interest for 1 year = $169.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $169.5 × 9 = $1525.5
Thus, Simple Interest (SI) = $1525.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $1525.5
= $7175.5
Thus, Amount to be paid = $7175.5 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.
(3) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.
(5) If Lisa paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(7) If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.
(10) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.