Question:
Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.
Correct Answer
$7048.5
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 3%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 9
= $5550 ×3/100 × 9
= 5550 × 3 × 9/100
= 16650 × 9/100
= 149850/100
= $1498.5
Thus, Simple Interest = $1498.5
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 + $1498.5
= $7048.5
Thus, Amount to be paid = $7048.5 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) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5550 + ($5550 × 3% × 9)
= $5550 + ($5550 ×3/100 × 9)
= $5550 + (5550 × 3 × 9/100)
= $5550 + (16650 × 9/100)
= $5550 + (149850/100)
= $5550 + $1498.5 = $7048.5
Thus, Amount (A) to be paid = $7048.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5550, the simple interest in 1 year
= 3/100 × 5550
= 3 × 5550/100
= 16650/100 = $166.5
Thus, simple interest for 1 year = $166.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $166.5 × 9 = $1498.5
Thus, Simple Interest (SI) = $1498.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $1498.5
= $7048.5
Thus, Amount to be paid = $7048.5 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(2) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.
(4) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(5) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.
(7) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.
(8) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 4% simple interest?
(10) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?