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 $9050 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) = 9% per annum

Amount (A) = $9050

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 = $9050 – $5000 = $4050

Thus, Simple Interest = $4050

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 × 4050}/_{5000 × 9}

= ⁴⁰⁵⁰⁰⁰/₄₅₀₀₀

= 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) = 9% per annum

Simple Interest = $4050 (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 $4050, then the time = ¹/₄₅₀ × 4050 years

= ^{1 × 4050}/₄₅₀ years

= ⁴⁰⁵⁰/₄₅₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?

(3) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?

(4) If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.

(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?

(7) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.

(8) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.

(9) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.