Question:
What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?
Correct Answer
$4312.5
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 5%
Time (t) = 5 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) = $3450 × 5% × 5
= $3450 ×5/100 × 5
= 3450 × 5 × 5/100
= 17250 × 5/100
= 86250/100
= $862.5
Thus, Simple Interest = $862.5
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 + $862.5
= $4312.5
Thus, Amount to be paid = $4312.5 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) = 5%
And, Time (t) = 5 years
Thus, Amount (A)
= $3450 + ($3450 × 5% × 5)
= $3450 + ($3450 ×5/100 × 5)
= $3450 + (3450 × 5 × 5/100)
= $3450 + (17250 × 5/100)
= $3450 + (86250/100)
= $3450 + $862.5 = $4312.5
Thus, Amount (A) to be paid = $4312.5 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 $3450, the simple interest in 1 year
= 5/100 × 3450
= 5 × 3450/100
= 17250/100 = $172.5
Thus, simple interest for 1 year = $172.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $172.5 × 5 = $862.5
Thus, Simple Interest (SI) = $862.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $862.5
= $4312.5
Thus, Amount to be paid = $4312.5 Answer
Similar Questions
(1) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.
(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?
(4) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.
(5) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(6) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?
(8) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(9) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.