Question:
What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?
Correct Answer
$5002.5
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 9%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $3450 × 9% × 5
= $3450 ×9/100 × 5
= 3450 × 9 × 5/100
= 31050 × 5/100
= 155250/100
= $1552.5
Thus, Simple Interest = $1552.5
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 = $3450 + $1552.5
= $5002.5
Thus, Amount to be paid = $5002.5 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 = $3450
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 5 years
Thus, Amount (A)
= $3450 + ($3450 × 9% × 5)
= $3450 + ($3450 ×9/100 × 5)
= $3450 + (3450 × 9 × 5/100)
= $3450 + (31050 × 5/100)
= $3450 + (155250/100)
= $3450 + $1552.5 = $5002.5
Thus, Amount (A) to be paid = $5002.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3450, the simple interest in 1 year
= 9/100 × 3450
= 9 × 3450/100
= 31050/100 = $310.5
Thus, simple interest for 1 year = $310.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $310.5 × 5 = $1552.5
Thus, Simple Interest (SI) = $1552.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1552.5
= $5002.5
Thus, Amount to be paid = $5002.5 Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?
(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 5% simple interest?
(5) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $13000 to clear the loan, then find the time period of the loan.
(6) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(7) How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?
(8) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(9) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?