Question:
Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.
Correct Answer
$5005
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 10%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 3
= $3850 ×10/100 × 3
= 3850 × 10 × 3/100
= 38500 × 3/100
= 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) = 10%
And, Time (t) = 3 years
Thus, Amount (A)
= $3850 + ($3850 × 10% × 3)
= $3850 + ($3850 ×10/100 × 3)
= $3850 + (3850 × 10 × 3/100)
= $3850 + (38500 × 3/100)
= $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 = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3850, the simple interest in 1 year
= 10/100 × 3850
= 10 × 3850/100
= 38500/100 = $385
Thus, simple interest for 1 year = $385
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $385 × 3 = $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 after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
(2) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 10% simple interest?
(4) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(5) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?
(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?
(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
(8) How much loan did Thomas borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7250 to clear it?
(9) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.