Question:
Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 7 years.
Correct Answer
$7822.5
Solution And Explanation
Solution
Given,
Principal (P) = $5250
Rate of Simple Interest (SI) = 7%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 7
= $5250 ×7/100 × 7
= 5250 × 7 × 7/100
= 36750 × 7/100
= 257250/100
= $2572.5
Thus, Simple Interest = $2572.5
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 + $2572.5
= $7822.5
Thus, Amount to be paid = $7822.5 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) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5250 + ($5250 × 7% × 7)
= $5250 + ($5250 ×7/100 × 7)
= $5250 + (5250 × 7 × 7/100)
= $5250 + (36750 × 7/100)
= $5250 + (257250/100)
= $5250 + $2572.5 = $7822.5
Thus, Amount (A) to be paid = $7822.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5250, the simple interest in 1 year
= 7/100 × 5250
= 7 × 5250/100
= 36750/100 = $367.5
Thus, simple interest for 1 year = $367.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $367.5 × 7 = $2572.5
Thus, Simple Interest (SI) = $2572.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5250 + $2572.5
= $7822.5
Thus, Amount to be paid = $7822.5 Answer
Similar Questions
(1) Betty had to pay $4887.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.
(3) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?
(4) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.
(5) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?
(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 3 years.
(9) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.