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) What amount does James have to pay after 6 years if he takes a loan of $3000 at 4% simple interest?
(2) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?
(4) If Susan borrowed $3650 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.
(8) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.
(9) How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 7 years.