Question:
Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
Correct Answer
$8557.5
Solution And Explanation
Solution
Given,
Principal (P) = $5250
Rate of Simple Interest (SI) = 7%
Time (t) = 9 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% × 9
= $5250 ×7/100 × 9
= 5250 × 7 × 9/100
= 36750 × 9/100
= 330750/100
= $3307.5
Thus, Simple Interest = $3307.5
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 + $3307.5
= $8557.5
Thus, Amount to be paid = $8557.5 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) = 9 years
Thus, Amount (A)
= $5250 + ($5250 × 7% × 9)
= $5250 + ($5250 ×7/100 × 9)
= $5250 + (5250 × 7 × 9/100)
= $5250 + (36750 × 9/100)
= $5250 + (330750/100)
= $5250 + $3307.5 = $8557.5
Thus, Amount (A) to be paid = $8557.5 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 9 years
= Simple interest for 1 year × 9
= $367.5 × 9 = $3307.5
Thus, Simple Interest (SI) = $3307.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5250 + $3307.5
= $8557.5
Thus, Amount to be paid = $8557.5 Answer
Similar Questions
(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.
(2) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(3) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?
(4) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.
(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?
(7) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(8) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?
(10) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.