Question:
What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?
Correct Answer
$5775
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 10%
Time (t) = 5 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% × 5
= $3850 ×10/100 × 5
= 3850 × 10 × 5/100
= 38500 × 5/100
= 192500/100
= $1925
Thus, Simple Interest = $1925
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 + $1925
= $5775
Thus, Amount to be paid = $5775 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) = 5 years
Thus, Amount (A)
= $3850 + ($3850 × 10% × 5)
= $3850 + ($3850 ×10/100 × 5)
= $3850 + (3850 × 10 × 5/100)
= $3850 + (38500 × 5/100)
= $3850 + (192500/100)
= $3850 + $1925 = $5775
Thus, Amount (A) to be paid = $5775 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 5 years
= Simple interest for 1 year × 5
= $385 × 5 = $1925
Thus, Simple Interest (SI) = $1925
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $1925
= $5775
Thus, Amount to be paid = $5775 Answer
Similar Questions
(1) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?
(2) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(4) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 3 years.
(6) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.
(8) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?
(9) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?
(10) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.