Question:
What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?
Correct Answer
$4692
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 6%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $3450 × 6% × 6
= $3450 ×6/100 × 6
= 3450 × 6 × 6/100
= 20700 × 6/100
= 124200/100
= $1242
Thus, Simple Interest = $1242
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 = $3450 + $1242
= $4692
Thus, Amount to be paid = $4692 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 = $3450
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 6 years
Thus, Amount (A)
= $3450 + ($3450 × 6% × 6)
= $3450 + ($3450 ×6/100 × 6)
= $3450 + (3450 × 6 × 6/100)
= $3450 + (20700 × 6/100)
= $3450 + (124200/100)
= $3450 + $1242 = $4692
Thus, Amount (A) to be paid = $4692 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3450, the simple interest in 1 year
= 6/100 × 3450
= 6 × 3450/100
= 20700/100 = $207
Thus, simple interest for 1 year = $207
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $207 × 6 = $1242
Thus, Simple Interest (SI) = $1242
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1242
= $4692
Thus, Amount to be paid = $4692 Answer
Similar Questions
(1) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?
(2) How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?
(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
(4) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?
(6) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?
(7) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(8) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.
(10) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.