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 $8840 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6500

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

Amount (A) = $8840

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 = $8840 – $6500 = $2340

Thus, Simple Interest = $2340

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 × 2340}/_{6500 × 6}

= ²³⁴⁰⁰⁰/₃₉₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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 = $2340 (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 $2340, then the time = ¹/₃₉₀ × 2340 years

= ^{1 × 2340}/₃₉₀ years

= ²³⁴⁰/₃₉₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?

(2) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 4 years.

(3) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?

(4) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?

(5) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.

(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.

(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.

(8) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 4 years.

(9) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?

(10) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.