Question:
What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?
Correct Answer
$4750
Solution And Explanation
Solution
Given,
Principal (P) = $3800
Rate of Simple Interest (SI) = 5%
Time (t) = 5 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% × 5
= $3800 ×5/100 × 5
= 3800 × 5 × 5/100
= 19000 × 5/100
= 95000/100
= $950
Thus, Simple Interest = $950
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 + $950
= $4750
Thus, Amount to be paid = $4750 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) = 5 years
Thus, Amount (A)
= $3800 + ($3800 × 5% × 5)
= $3800 + ($3800 ×5/100 × 5)
= $3800 + (3800 × 5 × 5/100)
= $3800 + (19000 × 5/100)
= $3800 + (95000/100)
= $3800 + $950 = $4750
Thus, Amount (A) to be paid = $4750 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 5 years
= Simple interest for 1 year × 5
= $190 × 5 = $950
Thus, Simple Interest (SI) = $950
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3800 + $950
= $4750
Thus, Amount to be paid = $4750 Answer
Similar Questions
(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.
(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
(3) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(4) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(5) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.
(8) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(9) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(10) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?