Question:
Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
Correct Answer
$7605
Solution And Explanation
Solution
Given,
Principal (P) = $5850
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) = $5850 × 3% × 10
= $5850 ×3/100 × 10
= 5850 × 3 × 10/100
= 17550 × 10/100
= 175500/100
= $1755
Thus, Simple Interest = $1755
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 = $5850 + $1755
= $7605
Thus, Amount to be paid = $7605 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 = $5850
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5850 + ($5850 × 3% × 10)
= $5850 + ($5850 ×3/100 × 10)
= $5850 + (5850 × 3 × 10/100)
= $5850 + (17550 × 10/100)
= $5850 + (175500/100)
= $5850 + $1755 = $7605
Thus, Amount (A) to be paid = $7605 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 $5850, the simple interest in 1 year
= 3/100 × 5850
= 3 × 5850/100
= 17550/100 = $175.5
Thus, simple interest for 1 year = $175.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $175.5 × 10 = $1755
Thus, Simple Interest (SI) = $1755
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $1755
= $7605
Thus, Amount to be paid = $7605 Answer
Similar Questions
(1) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?
(3) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.
(4) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.
(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?
(6) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(7) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.
(9) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(10) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?