Question:
What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?
Correct Answer
$3795
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 5%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 2
= $3450 ×5/100 × 2
= 3450 × 5 × 2/100
= 17250 × 2/100
= 34500/100
= $345
Thus, Simple Interest = $345
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 + $345
= $3795
Thus, Amount to be paid = $3795 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) = 5%
And, Time (t) = 2 years
Thus, Amount (A)
= $3450 + ($3450 × 5% × 2)
= $3450 + ($3450 ×5/100 × 2)
= $3450 + (3450 × 5 × 2/100)
= $3450 + (17250 × 2/100)
= $3450 + (34500/100)
= $3450 + $345 = $3795
Thus, Amount (A) to be paid = $3795 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3450, the simple interest in 1 year
= 5/100 × 3450
= 5 × 3450/100
= 17250/100 = $172.5
Thus, simple interest for 1 year = $172.5
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $172.5 × 2 = $345
Thus, Simple Interest (SI) = $345
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $345
= $3795
Thus, Amount to be paid = $3795 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(2) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(3) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 4 years.
(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.
(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(8) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8642 to clear the loan, then find the time period of the loan.
(9) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?
(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?