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) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(2) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 2% simple interest?
(3) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?
(4) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
(5) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(6) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(7) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.
(9) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.