Question:
Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.
Correct Answer
$4774
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 8%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 3
= $3850 ×8/100 × 3
= 3850 × 8 × 3/100
= 30800 × 3/100
= 92400/100
= $924
Thus, Simple Interest = $924
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 + $924
= $4774
Thus, Amount to be paid = $4774 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) = 8%
And, Time (t) = 3 years
Thus, Amount (A)
= $3850 + ($3850 × 8% × 3)
= $3850 + ($3850 ×8/100 × 3)
= $3850 + (3850 × 8 × 3/100)
= $3850 + (30800 × 3/100)
= $3850 + (92400/100)
= $3850 + $924 = $4774
Thus, Amount (A) to be paid = $4774 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $3850, the simple interest in 1 year
= 8/100 × 3850
= 8 × 3850/100
= 30800/100 = $308
Thus, simple interest for 1 year = $308
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $308 × 3 = $924
Thus, Simple Interest (SI) = $924
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $924
= $4774
Thus, Amount to be paid = $4774 Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.
(3) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?
(5) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(6) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(7) Kimberly had to pay $5347.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 7 years.
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.
(10) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.