Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5600

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $8736

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 = $8736 – $5600 = $3136

Thus, Simple Interest = $3136

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 × 3136}/_{5600 × 7}

= ³¹³⁶⁰⁰/₃₉₂₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $5600

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $3136 (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 = 7% of Principal

= 7% of $5600

= ⁷/₁₀₀ × 5600

= ^{7 × 5600}/₁₀₀

= ³⁹²⁰⁰/₁₀₀ = 392

Thus, simple Interest for 1 year = $392

Now,

∵ If the simple Interest is $392, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₂ years

∴ If the simple Interest is $3136, then the time = ¹/₃₉₂ × 3136 years

= ^{1 × 3136}/₃₉₂ years

= ³¹³⁶/₃₉₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?

(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?

(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.

(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.

(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?

(7) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.

(8) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?

(9) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?

(10) How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?