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) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.
(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?
(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(4) How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?
(5) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?
(6) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?
(7) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.
(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?
(10) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?