Simple Interest
Math MCQs

Question :    How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?

Correct Answer  $7850

Solution & Explanation

Solution

Given,

Amount (A) = $9812.5

Rate of Simple Interest (R) = 5%

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

$9812.5 = P (1 + 5% × 5)

⇒ $9812.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9812.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9812.5 = P (1 + ²⁵/₁₀₀)

⇒ $9812.5 = P (^{100 + 25}/₁₀₀)

⇒ $9812.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9812.5

⇒ P = ^9812.5/_¹²⁵/100

⇒ P = 9812.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9812.5 × 100}/₁₂₅

⇒ P = ⁹⁸¹²⁵⁰/₁₂₅

⇒ P = $7850

Thus, the sum borrowed (P) = $7850 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 9812.5, then the Principal = ¹⁰⁰/₁₂₅ × 9812.5

= ^{100 × 9812.5}/₁₂₅

= ⁹⁸¹²⁵⁰/₁₂₅

= 7850

Thus, Principal = $7850

Thus, the sum borrowed = $7850 Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.

(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 8 years.

(4) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 7 years.

(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.

(7) How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?

(8) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?

(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 3% simple interest?