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) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.
(3) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?
(5) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(6) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?
(7) 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?
(8) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 3 years.