Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4700

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $6956

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 = $6956 – $4700 = $2256

Thus, Simple Interest = $2256

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 × 2256}/_{4700 × 8}

= ²²⁵⁶⁰⁰/₃₇₆₀₀

= 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) = $4700

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $2256 (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 = 8% of Principal

= 8% of $4700

= ⁸/₁₀₀ × 4700

= ^{8 × 4700}/₁₀₀

= ³⁷⁶⁰⁰/₁₀₀ = 376

Thus, simple Interest for 1 year = $376

Now,

∵ If the simple Interest is $376, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₇₆ years

∴ If the simple Interest is $2256, then the time = ¹/₃₇₆ × 2256 years

= ^{1 × 2256}/₃₇₆ years

= ²²⁵⁶/₃₇₆ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.

(3) What amount does John have to pay after 5 years if he takes a loan of $3200 at 8% simple interest?

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

(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?

(6) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?

(7) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?

(8) If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.

(10) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?