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) Kenneth had to pay $5300 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?
(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(5) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 4 years.
(7) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(10) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.