Question:
What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?
Correct Answer
$5929
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 9%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 6
= $3850 ×9/100 × 6
= 3850 × 9 × 6/100
= 34650 × 6/100
= 207900/100
= $2079
Thus, Simple Interest = $2079
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 + $2079
= $5929
Thus, Amount to be paid = $5929 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) = 9%
And, Time (t) = 6 years
Thus, Amount (A)
= $3850 + ($3850 × 9% × 6)
= $3850 + ($3850 ×9/100 × 6)
= $3850 + (3850 × 9 × 6/100)
= $3850 + (34650 × 6/100)
= $3850 + (207900/100)
= $3850 + $2079 = $5929
Thus, Amount (A) to be paid = $5929 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3850, the simple interest in 1 year
= 9/100 × 3850
= 9 × 3850/100
= 34650/100 = $346.5
Thus, simple interest for 1 year = $346.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $346.5 × 6 = $2079
Thus, Simple Interest (SI) = $2079
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $2079
= $5929
Thus, Amount to be paid = $5929 Answer
Similar Questions
(1) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?
(2) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.
(4) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(5) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9685 to clear the loan, then find the time period of the loan.
(6) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(7) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(9) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
(10) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.