Question:
What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?
Correct Answer
$5538
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 7%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 6
= $3900 ×7/100 × 6
= 3900 × 7 × 6/100
= 27300 × 6/100
= 163800/100
= $1638
Thus, Simple Interest = $1638
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 + $1638
= $5538
Thus, Amount to be paid = $5538 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) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3900 + ($3900 × 7% × 6)
= $3900 + ($3900 ×7/100 × 6)
= $3900 + (3900 × 7 × 6/100)
= $3900 + (27300 × 6/100)
= $3900 + (163800/100)
= $3900 + $1638 = $5538
Thus, Amount (A) to be paid = $5538 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3900, the simple interest in 1 year
= 7/100 × 3900
= 7 × 3900/100
= 27300/100 = $273
Thus, simple interest for 1 year = $273
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $273 × 6 = $1638
Thus, Simple Interest (SI) = $1638
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1638
= $5538
Thus, Amount to be paid = $5538 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 $8330 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(3) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 3 years.
(4) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 2% simple interest?
(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 6% simple interest?
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.
(7) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?
(8) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 2% simple interest?
(10) 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.