Question:
What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?
Correct Answer
$3795
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 2%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 5
= $3450 ×2/100 × 5
= 3450 × 2 × 5/100
= 6900 × 5/100
= 34500/100
= $345
Thus, Simple Interest = $345
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 + $345
= $3795
Thus, Amount to be paid = $3795 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) = 2%
And, Time (t) = 5 years
Thus, Amount (A)
= $3450 + ($3450 × 2% × 5)
= $3450 + ($3450 ×2/100 × 5)
= $3450 + (3450 × 2 × 5/100)
= $3450 + (6900 × 5/100)
= $3450 + (34500/100)
= $3450 + $345 = $3795
Thus, Amount (A) to be paid = $3795 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $3450, the simple interest in 1 year
= 2/100 × 3450
= 2 × 3450/100
= 6900/100 = $69
Thus, simple interest for 1 year = $69
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $69 × 5 = $345
Thus, Simple Interest (SI) = $345
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $345
= $3795
Thus, Amount to be paid = $3795 Answer
Similar Questions
(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 4% simple interest?
(2) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 9% simple interest?
(3) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.
(6) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 8 years.
(8) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(9) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?
(10) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.