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) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?
(2) Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.
(4) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) If Nancy paid $4980 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?
(8) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?
(9) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.