Question:
What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 6% simple interest?
Correct Answer
$4485
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 6%
Time (t) = 5 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% × 5
= $3450 ×6/100 × 5
= 3450 × 6 × 5/100
= 20700 × 5/100
= 103500/100
= $1035
Thus, Simple Interest = $1035
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 + $1035
= $4485
Thus, Amount to be paid = $4485 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) = 5 years
Thus, Amount (A)
= $3450 + ($3450 × 6% × 5)
= $3450 + ($3450 ×6/100 × 5)
= $3450 + (3450 × 6 × 5/100)
= $3450 + (20700 × 5/100)
= $3450 + (103500/100)
= $3450 + $1035 = $4485
Thus, Amount (A) to be paid = $4485 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 5 years
= Simple interest for 1 year × 5
= $207 × 5 = $1035
Thus, Simple Interest (SI) = $1035
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1035
= $4485
Thus, Amount to be paid = $4485 Answer
Similar Questions
(1) If Kenneth paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(3) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
(5) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(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) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.
(8) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(9) 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.
(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?