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) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.

(2) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?

(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.

(4) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?

(5) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.

(6) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.

(8) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.

(9) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?

(10) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.