Simple Interest
Math MCQs

Question :    William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 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) = 10% per annum

Amount (A) = $9500

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 = $9500 – $5000 = $4500

Thus, Simple Interest = $4500

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 × 4500}/_{5000 × 10}

= ⁴⁵⁰⁰⁰⁰/₅₀₀₀₀

= 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) = 10% per annum

Simple Interest = $4500 (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 = 10% of Principal

= 10% of $5000

= ¹⁰/₁₀₀ × 5000

= ^{10 × 5000}/₁₀₀

= ⁵⁰⁰⁰⁰/₁₀₀ = 500

Thus, simple Interest for 1 year = $500

Now,

∵ If the simple Interest is $500, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₀₀ years

∴ If the simple Interest is $4500, then the time = ¹/₅₀₀ × 4500 years

= ^{1 × 4500}/₅₀₀ years

= ⁴⁵⁰⁰/₅₀₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.

(2) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?

(3) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.

(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.

(6) How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?

(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.

(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.

(9) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?

(10) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?