Question:
What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?
Correct Answer
$5520
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 10%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 6
= $3450 ×10/100 × 6
= 3450 × 10 × 6/100
= 34500 × 6/100
= 207000/100
= $2070
Thus, Simple Interest = $2070
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 + $2070
= $5520
Thus, Amount to be paid = $5520 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) = 10%
And, Time (t) = 6 years
Thus, Amount (A)
= $3450 + ($3450 × 10% × 6)
= $3450 + ($3450 ×10/100 × 6)
= $3450 + (3450 × 10 × 6/100)
= $3450 + (34500 × 6/100)
= $3450 + (207000/100)
= $3450 + $2070 = $5520
Thus, Amount (A) to be paid = $5520 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3450, the simple interest in 1 year
= 10/100 × 3450
= 10 × 3450/100
= 34500/100 = $345
Thus, simple interest for 1 year = $345
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $345 × 6 = $2070
Thus, Simple Interest (SI) = $2070
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $2070
= $5520
Thus, Amount to be paid = $5520 Answer
Similar Questions
(1) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?
(2) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(3) If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) If Lisa paid $4374 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 4 years.
(6) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?
(8) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 5% simple interest.