Question:
What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?
Correct Answer
$5070
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 5%
Time (t) = 6 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% × 6
= $3900 ×5/100 × 6
= 3900 × 5 × 6/100
= 19500 × 6/100
= 117000/100
= $1170
Thus, Simple Interest = $1170
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 + $1170
= $5070
Thus, Amount to be paid = $5070 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) = 6 years
Thus, Amount (A)
= $3900 + ($3900 × 5% × 6)
= $3900 + ($3900 ×5/100 × 6)
= $3900 + (3900 × 5 × 6/100)
= $3900 + (19500 × 6/100)
= $3900 + (117000/100)
= $3900 + $1170 = $5070
Thus, Amount (A) to be paid = $5070 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 6 years
= Simple interest for 1 year × 6
= $195 × 6 = $1170
Thus, Simple Interest (SI) = $1170
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1170
= $5070
Thus, Amount to be paid = $5070 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?
(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?
(4) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(5) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.
(7) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.
(10) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.