Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
Correct Answer
$8658
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 7%
Time (t) = 8 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% × 8
= $5550 ×7/100 × 8
= 5550 × 7 × 8/100
= 38850 × 8/100
= 310800/100
= $3108
Thus, Simple Interest = $3108
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 + $3108
= $8658
Thus, Amount to be paid = $8658 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) = 8 years
Thus, Amount (A)
= $5550 + ($5550 × 7% × 8)
= $5550 + ($5550 ×7/100 × 8)
= $5550 + (5550 × 7 × 8/100)
= $5550 + (38850 × 8/100)
= $5550 + (310800/100)
= $5550 + $3108 = $8658
Thus, Amount (A) to be paid = $8658 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 8 years
= Simple interest for 1 year × 8
= $388.5 × 8 = $3108
Thus, Simple Interest (SI) = $3108
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $3108
= $8658
Thus, Amount to be paid = $8658 Answer
Similar Questions
(1) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?
(3) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(4) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.
(7) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?
(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?