Question:
Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.
Correct Answer
$7208
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 9
= $5300 ×4/100 × 9
= 5300 × 4 × 9/100
= 21200 × 9/100
= 190800/100
= $1908
Thus, Simple Interest = $1908
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 + $1908
= $7208
Thus, Amount to be paid = $7208 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) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5300 + ($5300 × 4% × 9)
= $5300 + ($5300 ×4/100 × 9)
= $5300 + (5300 × 4 × 9/100)
= $5300 + (21200 × 9/100)
= $5300 + (190800/100)
= $5300 + $1908 = $7208
Thus, Amount (A) to be paid = $7208 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5300, the simple interest in 1 year
= 4/100 × 5300
= 4 × 5300/100
= 21200/100 = $212
Thus, simple interest for 1 year = $212
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $212 × 9 = $1908
Thus, Simple Interest (SI) = $1908
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1908
= $7208
Thus, Amount to be paid = $7208 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?
(2) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 3 years.
(4) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
(5) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(6) If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?
(8) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.
(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.