Simple Interest
Math MCQs

Question :    Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6500

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

Amount (A) = $10400

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 = $10400 – $6500 = $3900

Thus, Simple Interest = $3900

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 × 3900}/_{6500 × 6}

= ³⁹⁰⁰⁰⁰/₃₉₀₀₀

= 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) = $6500

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

Simple Interest = $3900 (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 $6500

= ⁶/₁₀₀ × 6500

= ^{6 × 6500}/₁₀₀

= ³⁹⁰⁰⁰/₁₀₀ = 390

Thus, simple Interest for 1 year = $390

Now,

∵ If the simple Interest is $390, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₀ years

∴ If the simple Interest is $3900, then the time = ¹/₃₉₀ × 3900 years

= ^{1 × 3900}/₃₉₀ years

= ³⁹⁰⁰/₃₉₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(2) If Paul paid $5640 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.

(5) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 7% simple interest?

(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.

(7) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.

(8) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.

(9) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.

(10) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.