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) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(2) How much loan did Kevin borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8165 to clear it?

(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?

(4) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 4 years.

(6) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?

(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(8) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?

(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?

(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?