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 $8460 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4700

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

Amount (A) = $8460

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 = $8460 – $4700 = $3760

Thus, Simple Interest = $3760

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 × 3760}/_{4700 × 8}

= ³⁷⁶⁰⁰⁰/₃₇₆₀₀

= 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) = $4700

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

Simple Interest = $3760 (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 $3760, then the time = ¹/₃₇₆ × 3760 years

= ^{1 × 3760}/₃₇₆ years

= ³⁷⁶⁰/₃₇₆ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.

(3) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.

(5) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 9% simple interest?

(6) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.

(7) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?

(8) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.

(9) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(10) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?