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) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?
(2) How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?
(3) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) If Barbara borrowed $3550 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.
(7) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(8) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(10) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.