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) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 3 years.
(2) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(3) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.
(4) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
(5) Jessica had to pay $4312.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?
(7) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(8) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?
(10) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?