Question:
Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
Correct Answer
$8120
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 5%
Time (t) = 9 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) = $5600 × 5% × 9
= $5600 ×5/100 × 9
= 5600 × 5 × 9/100
= 28000 × 9/100
= 252000/100
= $2520
Thus, Simple Interest = $2520
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 = $5600 + $2520
= $8120
Thus, Amount to be paid = $8120 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 = $5600
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5600 + ($5600 × 5% × 9)
= $5600 + ($5600 ×5/100 × 9)
= $5600 + (5600 × 5 × 9/100)
= $5600 + (28000 × 9/100)
= $5600 + (252000/100)
= $5600 + $2520 = $8120
Thus, Amount (A) to be paid = $8120 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 $5600, the simple interest in 1 year
= 5/100 × 5600
= 5 × 5600/100
= 28000/100 = $280
Thus, simple interest for 1 year = $280
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $280 × 9 = $2520
Thus, Simple Interest (SI) = $2520
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $2520
= $8120
Thus, Amount to be paid = $8120 Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.
(2) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?
(3) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 8 years.
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 10% simple interest?
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.
(7) How much loan did Emily borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8437.5 to clear it?
(8) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(9) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.