Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.
Correct Answer
$4002
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 4%
Time (t) = 4 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% × 4
= $3450 ×4/100 × 4
= 3450 × 4 × 4/100
= 13800 × 4/100
= 55200/100
= $552
Thus, Simple Interest = $552
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 + $552
= $4002
Thus, Amount to be paid = $4002 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) = 4 years
Thus, Amount (A)
= $3450 + ($3450 × 4% × 4)
= $3450 + ($3450 ×4/100 × 4)
= $3450 + (3450 × 4 × 4/100)
= $3450 + (13800 × 4/100)
= $3450 + (55200/100)
= $3450 + $552 = $4002
Thus, Amount (A) to be paid = $4002 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 4 years
= Simple interest for 1 year × 4
= $138 × 4 = $552
Thus, Simple Interest (SI) = $552
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $552
= $4002
Thus, Amount to be paid = $4002 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.
(2) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?
(3) Thomas had to pay $4370 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?
(5) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.
(7) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?
(9) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.