Simple Interest
Math MCQs

Question :    Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6600

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

Amount (A) = $9834

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 = $9834 – $6600 = $3234

Thus, Simple Interest = $3234

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 × 3234}/_{6600 × 7}

= ³²³⁴⁰⁰/₄₆₂₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $6600

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

Simple Interest = $3234 (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 $6600

= ⁷/₁₀₀ × 6600

= ^{7 × 6600}/₁₀₀

= ⁴⁶²⁰⁰/₁₀₀ = 462

Thus, simple Interest for 1 year = $462

Now,

∵ If the simple Interest is $462, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₂ years

∴ If the simple Interest is $3234, then the time = ¹/₄₆₂ × 3234 years

= ^{1 × 3234}/₄₆₂ years

= ³²³⁴/₄₆₂ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.

(2) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 7% simple interest?

(3) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?

(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 8 years.

(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.

(7) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.

(9) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 4 years.

(10) If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.