Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
Correct Answer
$3760.5
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 3%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 3
= $3450 ×3/100 × 3
= 3450 × 3 × 3/100
= 10350 × 3/100
= 31050/100
= $310.5
Thus, Simple Interest = $310.5
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 + $310.5
= $3760.5
Thus, Amount to be paid = $3760.5 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) = 3%
And, Time (t) = 3 years
Thus, Amount (A)
= $3450 + ($3450 × 3% × 3)
= $3450 + ($3450 ×3/100 × 3)
= $3450 + (3450 × 3 × 3/100)
= $3450 + (10350 × 3/100)
= $3450 + (31050/100)
= $3450 + $310.5 = $3760.5
Thus, Amount (A) to be paid = $3760.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3450, the simple interest in 1 year
= 3/100 × 3450
= 3 × 3450/100
= 10350/100 = $103.5
Thus, simple interest for 1 year = $103.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $103.5 × 3 = $310.5
Thus, Simple Interest (SI) = $310.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $310.5
= $3760.5
Thus, Amount to be paid = $3760.5 Answer
Similar Questions
(1) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.
(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?
(4) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.
(5) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.
(7) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
(9) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?
(10) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.