Question:
Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.
Correct Answer
$4928
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 7%
Time (t) = 4 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% × 4
= $3850 ×7/100 × 4
= 3850 × 7 × 4/100
= 26950 × 4/100
= 107800/100
= $1078
Thus, Simple Interest = $1078
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 + $1078
= $4928
Thus, Amount to be paid = $4928 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) = 4 years
Thus, Amount (A)
= $3850 + ($3850 × 7% × 4)
= $3850 + ($3850 ×7/100 × 4)
= $3850 + (3850 × 7 × 4/100)
= $3850 + (26950 × 4/100)
= $3850 + (107800/100)
= $3850 + $1078 = $4928
Thus, Amount (A) to be paid = $4928 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 4 years
= Simple interest for 1 year × 4
= $269.5 × 4 = $1078
Thus, Simple Interest (SI) = $1078
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $1078
= $4928
Thus, Amount to be paid = $4928 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 4 years.
(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(5) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(6) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(7) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?
(8) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(9) 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.
(10) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.