Question:
What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?
Correct Answer
$5265
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 7%
Time (t) = 5 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% × 5
= $3900 ×7/100 × 5
= 3900 × 7 × 5/100
= 27300 × 5/100
= 136500/100
= $1365
Thus, Simple Interest = $1365
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 + $1365
= $5265
Thus, Amount to be paid = $5265 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) = 5 years
Thus, Amount (A)
= $3900 + ($3900 × 7% × 5)
= $3900 + ($3900 ×7/100 × 5)
= $3900 + (3900 × 7 × 5/100)
= $3900 + (27300 × 5/100)
= $3900 + (136500/100)
= $3900 + $1365 = $5265
Thus, Amount (A) to be paid = $5265 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 5 years
= Simple interest for 1 year × 5
= $273 × 5 = $1365
Thus, Simple Interest (SI) = $1365
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1365
= $5265
Thus, Amount to be paid = $5265 Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.
(2) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.
(6) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(8) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?
(9) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(10) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.