Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.
Correct Answer
$4416
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 7%
Time (t) = 4 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) = $3450 × 7% × 4
= $3450 ×7/100 × 4
= 3450 × 7 × 4/100
= 24150 × 4/100
= 96600/100
= $966
Thus, Simple Interest = $966
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 + $966
= $4416
Thus, Amount to be paid = $4416 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) = 7%
And, Time (t) = 4 years
Thus, Amount (A)
= $3450 + ($3450 × 7% × 4)
= $3450 + ($3450 ×7/100 × 4)
= $3450 + (3450 × 7 × 4/100)
= $3450 + (24150 × 4/100)
= $3450 + (96600/100)
= $3450 + $966 = $4416
Thus, Amount (A) to be paid = $4416 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 $3450, the simple interest in 1 year
= 7/100 × 3450
= 7 × 3450/100
= 24150/100 = $241.5
Thus, simple interest for 1 year = $241.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $241.5 × 4 = $966
Thus, Simple Interest (SI) = $966
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $966
= $4416
Thus, Amount to be paid = $4416 Answer
Similar Questions
(1) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?
(2) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(3) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8528 to clear the loan, then find the time period of the loan.
(4) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 7% simple interest?
(6) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.
(7) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.
(8) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?
(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.