Question:
Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
Correct Answer
$4658.5
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 7%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $3850 × 7% × 3
= $3850 ×7/100 × 3
= 3850 × 7 × 3/100
= 26950 × 3/100
= 80850/100
= $808.5
Thus, Simple Interest = $808.5
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 = $3850 + $808.5
= $4658.5
Thus, Amount to be paid = $4658.5 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 = $3850
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 3 years
Thus, Amount (A)
= $3850 + ($3850 × 7% × 3)
= $3850 + ($3850 ×7/100 × 3)
= $3850 + (3850 × 7 × 3/100)
= $3850 + (26950 × 3/100)
= $3850 + (80850/100)
= $3850 + $808.5 = $4658.5
Thus, Amount (A) to be paid = $4658.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3850, the simple interest in 1 year
= 7/100 × 3850
= 7 × 3850/100
= 26950/100 = $269.5
Thus, simple interest for 1 year = $269.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $269.5 × 3 = $808.5
Thus, Simple Interest (SI) = $808.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $808.5
= $4658.5
Thus, Amount to be paid = $4658.5 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.
(2) If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(4) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(7) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 8 years.
(9) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(10) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.