Simple Interest
Math MCQs

Question :    William took a loan of $5000 at the rate of 9% 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  10

Solution & Explanation

Solution

Given,

Principal (P) = $5000

Rate of Simple Interest (R) = 9% 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 × 9}

= ⁴⁵⁰⁰⁰⁰/₄₅₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = 9% 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 = 9% of Principal

= 9% of $5000

= ⁹/₁₀₀ × 5000

= ^{9 × 5000}/₁₀₀

= ⁴⁵⁰⁰⁰/₁₀₀ = 450

Thus, simple Interest for 1 year = $450

Now,

∵ If the simple Interest is $450, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₀ years

∴ If the simple Interest is $4500, then the time = ¹/₄₅₀ × 4500 years

= ^{1 × 4500}/₄₅₀ years

= ⁴⁵⁰⁰/₄₅₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

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

(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?

(5) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?

(7) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.

(8) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 6% simple interest?

(10) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?