Question:
What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?
Correct Answer
$5070
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 6%
Time (t) = 5 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% × 5
= $3900 ×6/100 × 5
= 3900 × 6 × 5/100
= 23400 × 5/100
= 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) = 6%
And, Time (t) = 5 years
Thus, Amount (A)
= $3900 + ($3900 × 6% × 5)
= $3900 + ($3900 ×6/100 × 5)
= $3900 + (3900 × 6 × 5/100)
= $3900 + (23400 × 5/100)
= $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 = 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 5 years
= Simple interest for 1 year × 5
= $234 × 5 = $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) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?
(2) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?
(5) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(6) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 8 years.
(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?
(9) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(10) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.