Question:
What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?
Correct Answer
$4940
Solution And Explanation
Solution
Given,
Principal (P) = $3800
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) = $3800 × 5% × 6
= $3800 ×5/100 × 6
= 3800 × 5 × 6/100
= 19000 × 6/100
= 114000/100
= $1140
Thus, Simple Interest = $1140
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 + $1140
= $4940
Thus, Amount to be paid = $4940 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) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $3800 + ($3800 × 5% × 6)
= $3800 + ($3800 ×5/100 × 6)
= $3800 + (3800 × 5 × 6/100)
= $3800 + (19000 × 6/100)
= $3800 + (114000/100)
= $3800 + $1140 = $4940
Thus, Amount (A) to be paid = $4940 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 $3800, the simple interest in 1 year
= 5/100 × 3800
= 5 × 3800/100
= 19000/100 = $190
Thus, simple interest for 1 year = $190
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $190 × 6 = $1140
Thus, Simple Interest (SI) = $1140
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3800 + $1140
= $4940
Thus, Amount to be paid = $4940 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(2) Jessica had to pay $4087.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(5) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(6) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 8 years.
(8) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.
(10) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.