Question:
Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.
Correct Answer
$4602
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 6%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $3900 × 6% × 3
= $3900 ×6/100 × 3
= 3900 × 6 × 3/100
= 23400 × 3/100
= 70200/100
= $702
Thus, Simple Interest = $702
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 = $3900 + $702
= $4602
Thus, Amount to be paid = $4602 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 = $3900
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 3 years
Thus, Amount (A)
= $3900 + ($3900 × 6% × 3)
= $3900 + ($3900 ×6/100 × 3)
= $3900 + (3900 × 6 × 3/100)
= $3900 + (23400 × 3/100)
= $3900 + (70200/100)
= $3900 + $702 = $4602
Thus, Amount (A) to be paid = $4602 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3900, the simple interest in 1 year
= 6/100 × 3900
= 6 × 3900/100
= 23400/100 = $234
Thus, simple interest for 1 year = $234
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $234 × 3 = $702
Thus, Simple Interest (SI) = $702
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $702
= $4602
Thus, Amount to be paid = $4602 Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 5% simple interest?
(5) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(6) What amount does David have to pay after 6 years if he takes a loan of $3400 at 4% simple interest?
(7) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(8) Mark had to pay $4664 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?
(10) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.