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) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.
(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?
(3) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?
(4) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?
(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 4% simple interest?
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.
(7) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.
(9) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.