Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.
Correct Answer
$7770
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 8
= $5550 ×5/100 × 8
= 5550 × 5 × 8/100
= 27750 × 8/100
= 222000/100
= $2220
Thus, Simple Interest = $2220
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 + $2220
= $7770
Thus, Amount to be paid = $7770 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5550 + ($5550 × 5% × 8)
= $5550 + ($5550 ×5/100 × 8)
= $5550 + (5550 × 5 × 8/100)
= $5550 + (27750 × 8/100)
= $5550 + (222000/100)
= $5550 + $2220 = $7770
Thus, Amount (A) to be paid = $7770 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5550, the simple interest in 1 year
= 5/100 × 5550
= 5 × 5550/100
= 27750/100 = $277.5
Thus, simple interest for 1 year = $277.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $277.5 × 8 = $2220
Thus, Simple Interest (SI) = $2220
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $2220
= $7770
Thus, Amount to be paid = $7770 Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.
(2) How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?
(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?
(4) If Paul paid $5076 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 James borrowed a sum of $5000 at 9% simple interest for 8 years.
(6) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?
(7) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 8% simple interest?
(8) William had to pay $3815 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.