Simple Interest
Math MCQs

Question :    How much loan did Ashley borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7532.5 to clear it?

Correct Answer  $6550

Solution & Explanation

Solution

Given,

Amount (A) = $7532.5

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

$7532.5 = P (1 + 3% × 5)

⇒ $7532.5 = P (1 + ³/₁₀₀ × 5)

⇒ $7532.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7532.5 = P (1 + ¹⁵/₁₀₀)

⇒ $7532.5 = P (^{100 + 15}/₁₀₀)

⇒ $7532.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7532.5

⇒ P = ^7532.5/_¹¹⁵/100

⇒ P = 7532.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{7532.5 × 100}/₁₁₅

⇒ P = ⁷⁵³²⁵⁰/₁₁₅

⇒ P = $6550

Thus, the sum borrowed (P) = $6550 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 7532.5, then the Principal = ¹⁰⁰/₁₁₅ × 7532.5

= ^{100 × 7532.5}/₁₁₅

= ⁷⁵³²⁵⁰/₁₁₅

= 6550

Thus, Principal = $6550

Thus, the sum borrowed = $6550 Answer

Similar Questions

(1) 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.

(2) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.

(4) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(5) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?

(7) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.

(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 4 years.

(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.