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 will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?
(2) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
(4) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?
(7) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?
(8) If Karen borrowed $3950 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?
(10) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?