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) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
(2) How much loan did Sandra borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8062.5 to clear it?
(3) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.
(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?
(5) If Karen borrowed $3950 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(7) 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.
(8) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.
(10) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.