Question:
What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?
Correct Answer
$5175
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 10%
Time (t) = 5 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% × 5
= $3450 ×10/100 × 5
= 3450 × 10 × 5/100
= 34500 × 5/100
= 172500/100
= $1725
Thus, Simple Interest = $1725
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 + $1725
= $5175
Thus, Amount to be paid = $5175 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) = 5 years
Thus, Amount (A)
= $3450 + ($3450 × 10% × 5)
= $3450 + ($3450 ×10/100 × 5)
= $3450 + (3450 × 10 × 5/100)
= $3450 + (34500 × 5/100)
= $3450 + (172500/100)
= $3450 + $1725 = $5175
Thus, Amount (A) to be paid = $5175 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 5 years
= Simple interest for 1 year × 5
= $345 × 5 = $1725
Thus, Simple Interest (SI) = $1725
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1725
= $5175
Thus, Amount to be paid = $5175 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(2) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(4) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(5) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(6) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 8 years.
(10) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.