Simple Interest
MCQs Math


Question:     How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?


Correct Answer  $5350

Solution And Explanation

Solution

Given,

Amount (A) = $6152.5

Rate of Simple Interest (R) = 3%

Time (T) = 5 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$6152.5 = P (1 + 3% × 5)

⇒ $6152.5 = P (1 + 3/100 × 5)

⇒ $6152.5 = P (1 + 3 × 5/100)

⇒ $6152.5 = P (1 + 15/100)

⇒ $6152.5 = P (100 + 15/100)

⇒ $6152.5 = P × 115/100

⇒ P × 115/100 = $6152.5

⇒ P = 6152.5/115/100

⇒ P = 6152.5 × 100/115

⇒ P = 6152.5 × 100/115

⇒ P = 615250/115

⇒ P = $5350

Thus, the sum borrowed (P) = $5350 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/115

∴ If the Amount is 6152.5, then the Principal = 100/115 × 6152.5

= 100 × 6152.5/115

= 615250/115

= 5350

Thus, Principal = $5350

Thus, the sum borrowed = $5350 Answer


Similar Questions

(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?

(2) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?

(4) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.

(5) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.

(6) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.

(7) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?

(8) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.

(9) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.

(10) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.


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