Simple Interest
Math MCQs

Question :    How much loan did Sandra borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8062.5 to clear it?

Correct Answer  $6450

Solution & Explanation

Solution

Given,

Amount (A) = $8062.5

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

$8062.5 = P (1 + 5% × 5)

⇒ $8062.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8062.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8062.5 = P (1 + ²⁵/₁₀₀)

⇒ $8062.5 = P (^{100 + 25}/₁₀₀)

⇒ $8062.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8062.5

⇒ P = ^8062.5/_¹²⁵/100

⇒ P = 8062.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{8062.5 × 100}/₁₂₅

⇒ P = ⁸⁰⁶²⁵⁰/₁₂₅

⇒ P = $6450

Thus, the sum borrowed (P) = $6450 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 8062.5, then the Principal = ¹⁰⁰/₁₂₅ × 8062.5

= ^{100 × 8062.5}/₁₂₅

= ⁸⁰⁶²⁵⁰/₁₂₅

= 6450

Thus, Principal = $6450

Thus, the sum borrowed = $6450 Answer

Similar Questions

(1) 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?

(2) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?

(3) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

(4) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?

(5) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?

(6) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?

(7) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 7 years.

(10) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.