Simple Interest
Math MCQs

Question :    How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?

Correct Answer  $6800

Solution & Explanation

Solution

Given,

Amount (A) = $8160

Rate of Simple Interest (R) = 4%

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

$8160 = P (1 + 4% × 5)

⇒ $8160 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8160 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8160 = P (1 + ²⁰/₁₀₀)

⇒ $8160 = P (^{100 + 20}/₁₀₀)

⇒ $8160 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8160

⇒ P = ⁸¹⁶⁰/_¹²⁰/100

⇒ P = 8160 × ¹⁰⁰/₁₂₀

⇒ P = ^{8160 × 100}/₁₂₀

⇒ P = ⁸¹⁶⁰⁰⁰/₁₂₀

⇒ P = $6800

Thus, the sum borrowed (P) = $6800 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 8160, then the Principal = ¹⁰⁰/₁₂₀ × 8160

= ^{100 × 8160}/₁₂₀

= ⁸¹⁶⁰⁰⁰/₁₂₀

= 6800

Thus, Principal = $6800

Thus, the sum borrowed = $6800 Answer

Similar Questions

(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.

(2) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.

(3) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?

(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 8 years.

(6) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.

(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.

(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.

(9) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.

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