Simple Interest
Math MCQs

Question :    How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?

Correct Answer  $5250

Solution & Explanation

Solution

Given,

Amount (A) = $6562.5

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

$6562.5 = P (1 + 5% × 5)

⇒ $6562.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6562.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6562.5 = P (1 + ²⁵/₁₀₀)

⇒ $6562.5 = P (^{100 + 25}/₁₀₀)

⇒ $6562.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6562.5

⇒ P = ^6562.5/_¹²⁵/100

⇒ P = 6562.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{6562.5 × 100}/₁₂₅

⇒ P = ⁶⁵⁶²⁵⁰/₁₂₅

⇒ P = $5250

Thus, the sum borrowed (P) = $5250 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 6562.5, then the Principal = ¹⁰⁰/₁₂₅ × 6562.5

= ^{100 × 6562.5}/₁₂₅

= ⁶⁵⁶²⁵⁰/₁₂₅

= 5250

Thus, Principal = $5250

Thus, the sum borrowed = $5250 Answer

Similar Questions

(1) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 10% simple interest?

(2) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

(3) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

(4) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.

(6) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.