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) How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?
(2) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.
(4) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.
(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(6) If Sandra paid $4806 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?
(8) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(10) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.