Question:
Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.
Correct Answer
$7455
Solution And Explanation
Solution
Given,
Principal (P) = $5250
Rate of Simple Interest (SI) = 6%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5250 × 6% × 7
= $5250 ×6/100 × 7
= 5250 × 6 × 7/100
= 31500 × 7/100
= 220500/100
= $2205
Thus, Simple Interest = $2205
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 = $5250 + $2205
= $7455
Thus, Amount to be paid = $7455 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 = $5250
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 7 years
Thus, Amount (A)
= $5250 + ($5250 × 6% × 7)
= $5250 + ($5250 ×6/100 × 7)
= $5250 + (5250 × 6 × 7/100)
= $5250 + (31500 × 7/100)
= $5250 + (220500/100)
= $5250 + $2205 = $7455
Thus, Amount (A) to be paid = $7455 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5250, the simple interest in 1 year
= 6/100 × 5250
= 6 × 5250/100
= 31500/100 = $315
Thus, simple interest for 1 year = $315
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $315 × 7 = $2205
Thus, Simple Interest (SI) = $2205
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5250 + $2205
= $7455
Thus, Amount to be paid = $7455 Answer
Similar Questions
(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 7% simple interest?
(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?
(4) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(5) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(6) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.
(7) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(8) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?
(10) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?