Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $9955

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 = $9955 – $5500 = $4455

Thus, Simple Interest = $4455

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 × 4455}/_{5500 × 9}

= ⁴⁴⁵⁵⁰⁰/₄₉₅₀₀

= 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) = $5500

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $4455 (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 $5500

= ⁹/₁₀₀ × 5500

= ^{9 × 5500}/₁₀₀

= ⁴⁹⁵⁰⁰/₁₀₀ = 495

Thus, simple Interest for 1 year = $495

Now,

∵ If the simple Interest is $495, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₉₅ years

∴ If the simple Interest is $4455, then the time = ¹/₄₉₅ × 4455 years

= ^{1 × 4455}/₄₉₅ years

= ⁴⁴⁵⁵/₄₉₅ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(2) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?

(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.

(5) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?

(6) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 3 years.

(9) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.