Question:
What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?
Correct Answer
$4140
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 4%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 5
= $3450 ×4/100 × 5
= 3450 × 4 × 5/100
= 13800 × 5/100
= 69000/100
= $690
Thus, Simple Interest = $690
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 + $690
= $4140
Thus, Amount to be paid = $4140 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) = 4%
And, Time (t) = 5 years
Thus, Amount (A)
= $3450 + ($3450 × 4% × 5)
= $3450 + ($3450 ×4/100 × 5)
= $3450 + (3450 × 4 × 5/100)
= $3450 + (13800 × 5/100)
= $3450 + (69000/100)
= $3450 + $690 = $4140
Thus, Amount (A) to be paid = $4140 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3450, the simple interest in 1 year
= 4/100 × 3450
= 4 × 3450/100
= 13800/100 = $138
Thus, simple interest for 1 year = $138
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $138 × 5 = $690
Thus, Simple Interest (SI) = $690
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $690
= $4140
Thus, Amount to be paid = $4140 Answer
Similar Questions
(1) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?
(2) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?
(3) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(4) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.
(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(7) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.