Question:
What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?
Correct Answer
$4071
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 3%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 6
= $3450 ×3/100 × 6
= 3450 × 3 × 6/100
= 10350 × 6/100
= 62100/100
= $621
Thus, Simple Interest = $621
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 + $621
= $4071
Thus, Amount to be paid = $4071 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) = 3%
And, Time (t) = 6 years
Thus, Amount (A)
= $3450 + ($3450 × 3% × 6)
= $3450 + ($3450 ×3/100 × 6)
= $3450 + (3450 × 3 × 6/100)
= $3450 + (10350 × 6/100)
= $3450 + (62100/100)
= $3450 + $621 = $4071
Thus, Amount (A) to be paid = $4071 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3450, the simple interest in 1 year
= 3/100 × 3450
= 3 × 3450/100
= 10350/100 = $103.5
Thus, simple interest for 1 year = $103.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $103.5 × 6 = $621
Thus, Simple Interest (SI) = $621
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $621
= $4071
Thus, Amount to be paid = $4071 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.
(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?
(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(4) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
(5) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.
(9) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?