Question:
Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
Correct Answer
$6890
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 3%
Time (t) = 10 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) = $5300 × 3% × 10
= $5300 ×3/100 × 10
= 5300 × 3 × 10/100
= 15900 × 10/100
= 159000/100
= $1590
Thus, Simple Interest = $1590
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 = $5300 + $1590
= $6890
Thus, Amount to be paid = $6890 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 = $5300
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5300 + ($5300 × 3% × 10)
= $5300 + ($5300 ×3/100 × 10)
= $5300 + (5300 × 3 × 10/100)
= $5300 + (15900 × 10/100)
= $5300 + (159000/100)
= $5300 + $1590 = $6890
Thus, Amount (A) to be paid = $6890 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 $5300, the simple interest in 1 year
= 3/100 × 5300
= 3 × 5300/100
= 15900/100 = $159
Thus, simple interest for 1 year = $159
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $159 × 10 = $1590
Thus, Simple Interest (SI) = $1590
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1590
= $6890
Thus, Amount to be paid = $6890 Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 4 years.
(2) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(4) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(6) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?
(7) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(8) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(9) What amount does David have to pay after 5 years if he takes a loan of $3400 at 3% simple interest?
(10) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.