Question:
Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
Correct Answer
$7685
Solution And Explanation
Solution
Given,
Principal (P) = $5300
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) = $5300 × 5% × 9
= $5300 ×5/100 × 9
= 5300 × 5 × 9/100
= 26500 × 9/100
= 238500/100
= $2385
Thus, Simple Interest = $2385
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 = $5300 + $2385
= $7685
Thus, Amount to be paid = $7685 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 = $5300
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5300 + ($5300 × 5% × 9)
= $5300 + ($5300 ×5/100 × 9)
= $5300 + (5300 × 5 × 9/100)
= $5300 + (26500 × 9/100)
= $5300 + (238500/100)
= $5300 + $2385 = $7685
Thus, Amount (A) to be paid = $7685 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 $5300, the simple interest in 1 year
= 5/100 × 5300
= 5 × 5300/100
= 26500/100 = $265
Thus, simple interest for 1 year = $265
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $265 × 9 = $2385
Thus, Simple Interest (SI) = $2385
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2385
= $7685
Thus, Amount to be paid = $7685 Answer
Similar Questions
(1) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.
(2) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?
(3) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.
(7) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?
(8) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.
(10) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?