Question:
Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.
Correct Answer
$8625
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 5%
Time (t) = 10 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) = $5750 × 5% × 10
= $5750 ×5/100 × 10
= 5750 × 5 × 10/100
= 28750 × 10/100
= 287500/100
= $2875
Thus, Simple Interest = $2875
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 = $5750 + $2875
= $8625
Thus, Amount to be paid = $8625 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 = $5750
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5750 + ($5750 × 5% × 10)
= $5750 + ($5750 ×5/100 × 10)
= $5750 + (5750 × 5 × 10/100)
= $5750 + (28750 × 10/100)
= $5750 + (287500/100)
= $5750 + $2875 = $8625
Thus, Amount (A) to be paid = $8625 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 $5750, the simple interest in 1 year
= 5/100 × 5750
= 5 × 5750/100
= 28750/100 = $287.5
Thus, simple interest for 1 year = $287.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $287.5 × 10 = $2875
Thus, Simple Interest (SI) = $2875
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $2875
= $8625
Thus, Amount to be paid = $8625 Answer
Similar Questions
(1) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 8% simple interest?
(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.
(3) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(4) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 4 years.
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.
(7) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(8) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.
(10) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.