Question:
Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
Correct Answer
$9046.5
Solution And Explanation
Solution
Given,
Principal (P) = $5550
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) = $5550 × 7% × 9
= $5550 ×7/100 × 9
= 5550 × 7 × 9/100
= 38850 × 9/100
= 349650/100
= $3496.5
Thus, Simple Interest = $3496.5
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 = $5550 + $3496.5
= $9046.5
Thus, Amount to be paid = $9046.5 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 = $5550
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5550 + ($5550 × 7% × 9)
= $5550 + ($5550 ×7/100 × 9)
= $5550 + (5550 × 7 × 9/100)
= $5550 + (38850 × 9/100)
= $5550 + (349650/100)
= $5550 + $3496.5 = $9046.5
Thus, Amount (A) to be paid = $9046.5 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 $5550, the simple interest in 1 year
= 7/100 × 5550
= 7 × 5550/100
= 38850/100 = $388.5
Thus, simple interest for 1 year = $388.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $388.5 × 9 = $3496.5
Thus, Simple Interest (SI) = $3496.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $3496.5
= $9046.5
Thus, Amount to be paid = $9046.5 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(2) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?
(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?
(4) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.
(7) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 4 years.
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 8 years.
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.
(10) How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?