Question:
Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.
Correct Answer
$5082
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 8%
Time (t) = 4 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% × 4
= $3850 ×8/100 × 4
= 3850 × 8 × 4/100
= 30800 × 4/100
= 123200/100
= $1232
Thus, Simple Interest = $1232
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 + $1232
= $5082
Thus, Amount to be paid = $5082 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) = 4 years
Thus, Amount (A)
= $3850 + ($3850 × 8% × 4)
= $3850 + ($3850 ×8/100 × 4)
= $3850 + (3850 × 8 × 4/100)
= $3850 + (30800 × 4/100)
= $3850 + (123200/100)
= $3850 + $1232 = $5082
Thus, Amount (A) to be paid = $5082 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 4 years
= Simple interest for 1 year × 4
= $308 × 4 = $1232
Thus, Simple Interest (SI) = $1232
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $1232
= $5082
Thus, Amount to be paid = $5082 Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.
(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?
(3) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(5) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(6) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(7) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11152 to clear the loan, then find the time period of the loan.
(8) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(9) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(10) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?