Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.
Correct Answer
$3967.5
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 5%
Time (t) = 3 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% × 3
= $3450 ×5/100 × 3
= 3450 × 5 × 3/100
= 17250 × 3/100
= 51750/100
= $517.5
Thus, Simple Interest = $517.5
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 + $517.5
= $3967.5
Thus, Amount to be paid = $3967.5 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) = 3 years
Thus, Amount (A)
= $3450 + ($3450 × 5% × 3)
= $3450 + ($3450 ×5/100 × 3)
= $3450 + (3450 × 5 × 3/100)
= $3450 + (17250 × 3/100)
= $3450 + (51750/100)
= $3450 + $517.5 = $3967.5
Thus, Amount (A) to be paid = $3967.5 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 3 years
= Simple interest for 1 year × 3
= $172.5 × 3 = $517.5
Thus, Simple Interest (SI) = $517.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $517.5
= $3967.5
Thus, Amount to be paid = $3967.5 Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(2) 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.
(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 3% simple interest?
(4) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?
(6) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?
(7) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(10) 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.