Question:
What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?
Correct Answer
$5396
Solution And Explanation
Solution
Given,
Principal (P) = $3800
Rate of Simple Interest (SI) = 7%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 6
= $3800 ×7/100 × 6
= 3800 × 7 × 6/100
= 26600 × 6/100
= 159600/100
= $1596
Thus, Simple Interest = $1596
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 + $1596
= $5396
Thus, Amount to be paid = $5396 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) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3800 + ($3800 × 7% × 6)
= $3800 + ($3800 ×7/100 × 6)
= $3800 + (3800 × 7 × 6/100)
= $3800 + (26600 × 6/100)
= $3800 + (159600/100)
= $3800 + $1596 = $5396
Thus, Amount (A) to be paid = $5396 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3800, the simple interest in 1 year
= 7/100 × 3800
= 7 × 3800/100
= 26600/100 = $266
Thus, simple interest for 1 year = $266
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $266 × 6 = $1596
Thus, Simple Interest (SI) = $1596
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3800 + $1596
= $5396
Thus, Amount to be paid = $5396 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?
(2) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.
(4) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(5) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(6) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.
(9) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(10) How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?