Question:
What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?
Correct Answer
$5700
Solution And Explanation
Solution
Given,
Principal (P) = $3800
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) = $3800 × 10% × 5
= $3800 ×10/100 × 5
= 3800 × 10 × 5/100
= 38000 × 5/100
= 190000/100
= $1900
Thus, Simple Interest = $1900
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 = $3800 + $1900
= $5700
Thus, Amount to be paid = $5700 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 = $3800
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 5 years
Thus, Amount (A)
= $3800 + ($3800 × 10% × 5)
= $3800 + ($3800 ×10/100 × 5)
= $3800 + (3800 × 10 × 5/100)
= $3800 + (38000 × 5/100)
= $3800 + (190000/100)
= $3800 + $1900 = $5700
Thus, Amount (A) to be paid = $5700 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 $3800, the simple interest in 1 year
= 10/100 × 3800
= 10 × 3800/100
= 38000/100 = $380
Thus, simple interest for 1 year = $380
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $380 × 5 = $1900
Thus, Simple Interest (SI) = $1900
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3800 + $1900
= $5700
Thus, Amount to be paid = $5700 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(2) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 8 years.
(4) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.
(5) 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.
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.
(7) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.
(10) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.