Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.
Correct Answer
$7965
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 5%
Time (t) = 7 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) = $5900 × 5% × 7
= $5900 ×5/100 × 7
= 5900 × 5 × 7/100
= 29500 × 7/100
= 206500/100
= $2065
Thus, Simple Interest = $2065
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 = $5900 + $2065
= $7965
Thus, Amount to be paid = $7965 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 = $5900
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5900 + ($5900 × 5% × 7)
= $5900 + ($5900 ×5/100 × 7)
= $5900 + (5900 × 5 × 7/100)
= $5900 + (29500 × 7/100)
= $5900 + (206500/100)
= $5900 + $2065 = $7965
Thus, Amount (A) to be paid = $7965 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 $5900, the simple interest in 1 year
= 5/100 × 5900
= 5 × 5900/100
= 29500/100 = $295
Thus, simple interest for 1 year = $295
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $295 × 7 = $2065
Thus, Simple Interest (SI) = $2065
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $2065
= $7965
Thus, Amount to be paid = $7965 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(2) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 3 years.
(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
(5) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 8 years.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.
(8) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 7 years.
(10) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.