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) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(2) Elizabeth had to pay $3864 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?
(5) John had to pay $3584 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Donna had to pay $5141 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?
(9) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.