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) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
(2) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?
(3) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.
(5) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?
(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.
(7) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.
(9) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?