Simple Interest
Math MCQs

Question :    William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5000

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $7700

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $7700 – $5000 = $2700

Thus, Simple Interest = $2700

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 2700}/_{5000 × 6}

= ²⁷⁰⁰⁰⁰/₃₀₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $5000

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2700 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 6% of Principal

= 6% of $5000

= ⁶/₁₀₀ × 5000

= ^{6 × 5000}/₁₀₀

= ³⁰⁰⁰⁰/₁₀₀ = 300

Thus, simple Interest for 1 year = $300

Now,

∵ If the simple Interest is $300, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₀ years

∴ If the simple Interest is $2700, then the time = ¹/₃₀₀ × 2700 years

= ^{1 × 2700}/₃₀₀ years

= ²⁷⁰⁰/₃₀₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(2) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.

(5) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.

(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?

(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.

(9) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?