Question:
Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
Correct Answer
$7475
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 3%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 10
= $5750 ×3/100 × 10
= 5750 × 3 × 10/100
= 17250 × 10/100
= 172500/100
= $1725
Thus, Simple Interest = $1725
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 + $1725
= $7475
Thus, Amount to be paid = $7475 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) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5750 + ($5750 × 3% × 10)
= $5750 + ($5750 ×3/100 × 10)
= $5750 + (5750 × 3 × 10/100)
= $5750 + (17250 × 10/100)
= $5750 + (172500/100)
= $5750 + $1725 = $7475
Thus, Amount (A) to be paid = $7475 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5750, the simple interest in 1 year
= 3/100 × 5750
= 3 × 5750/100
= 17250/100 = $172.5
Thus, simple interest for 1 year = $172.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $172.5 × 10 = $1725
Thus, Simple Interest (SI) = $1725
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $1725
= $7475
Thus, Amount to be paid = $7475 Answer
Similar Questions
(1) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?
(2) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.
(4) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(5) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?
(6) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?
(8) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.
(9) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?