Question:
What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?
Correct Answer
$4875
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 5%
Time (t) = 5 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) = $3900 × 5% × 5
= $3900 ×5/100 × 5
= 3900 × 5 × 5/100
= 19500 × 5/100
= 97500/100
= $975
Thus, Simple Interest = $975
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 + $975
= $4875
Thus, Amount to be paid = $4875 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) = 5%
And, Time (t) = 5 years
Thus, Amount (A)
= $3900 + ($3900 × 5% × 5)
= $3900 + ($3900 ×5/100 × 5)
= $3900 + (3900 × 5 × 5/100)
= $3900 + (19500 × 5/100)
= $3900 + (97500/100)
= $3900 + $975 = $4875
Thus, Amount (A) to be paid = $4875 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 $3900, the simple interest in 1 year
= 5/100 × 3900
= 5 × 3900/100
= 19500/100 = $195
Thus, simple interest for 1 year = $195
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $195 × 5 = $975
Thus, Simple Interest (SI) = $975
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $975
= $4875
Thus, Amount to be paid = $4875 Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?
(2) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?
(4) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?
(6) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
(7) If Steven paid $5152 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 7 years.
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.
(10) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.