Question:
What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?
Correct Answer
$5005
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 5%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 6
= $3850 ×5/100 × 6
= 3850 × 5 × 6/100
= 19250 × 6/100
= 115500/100
= $1155
Thus, Simple Interest = $1155
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 + $1155
= $5005
Thus, Amount to be paid = $5005 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) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $3850 + ($3850 × 5% × 6)
= $3850 + ($3850 ×5/100 × 6)
= $3850 + (3850 × 5 × 6/100)
= $3850 + (19250 × 6/100)
= $3850 + (115500/100)
= $3850 + $1155 = $5005
Thus, Amount (A) to be paid = $5005 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3850, the simple interest in 1 year
= 5/100 × 3850
= 5 × 3850/100
= 19250/100 = $192.5
Thus, simple interest for 1 year = $192.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $192.5 × 6 = $1155
Thus, Simple Interest (SI) = $1155
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $1155
= $5005
Thus, Amount to be paid = $5005 Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.
(2) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(3) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?
(4) 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.
(5) How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?
(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(7) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.
(8) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
(9) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.
(10) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?