Question:
Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
Correct Answer
$8190
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 4%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 10
= $5850 ×4/100 × 10
= 5850 × 4 × 10/100
= 23400 × 10/100
= 234000/100
= $2340
Thus, Simple Interest = $2340
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 + $2340
= $8190
Thus, Amount to be paid = $8190 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) = 4%
And, Time (t) = 10 years
Thus, Amount (A)
= $5850 + ($5850 × 4% × 10)
= $5850 + ($5850 ×4/100 × 10)
= $5850 + (5850 × 4 × 10/100)
= $5850 + (23400 × 10/100)
= $5850 + (234000/100)
= $5850 + $2340 = $8190
Thus, Amount (A) to be paid = $8190 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5850, the simple interest in 1 year
= 4/100 × 5850
= 4 × 5850/100
= 23400/100 = $234
Thus, simple interest for 1 year = $234
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $234 × 10 = $2340
Thus, Simple Interest (SI) = $2340
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $2340
= $8190
Thus, Amount to be paid = $8190 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 8 years.
(5) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(6) If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(8) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(10) 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.