Question:
What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?
Correct Answer
$5236
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 6%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 6
= $3850 ×6/100 × 6
= 3850 × 6 × 6/100
= 23100 × 6/100
= 138600/100
= $1386
Thus, Simple Interest = $1386
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 + $1386
= $5236
Thus, Amount to be paid = $5236 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) = 6%
And, Time (t) = 6 years
Thus, Amount (A)
= $3850 + ($3850 × 6% × 6)
= $3850 + ($3850 ×6/100 × 6)
= $3850 + (3850 × 6 × 6/100)
= $3850 + (23100 × 6/100)
= $3850 + (138600/100)
= $3850 + $1386 = $5236
Thus, Amount (A) to be paid = $5236 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3850, the simple interest in 1 year
= 6/100 × 3850
= 6 × 3850/100
= 23100/100 = $231
Thus, simple interest for 1 year = $231
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $231 × 6 = $1386
Thus, Simple Interest (SI) = $1386
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $1386
= $5236
Thus, Amount to be paid = $5236 Answer
Similar Questions
(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.
(3) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(5) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?
(7) How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?
(8) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?
(9) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(10) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?