Simple Interest
Math MCQs

Question :    Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6800

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

Amount (A) = $11084

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 = $11084 – $6800 = $4284

Thus, Simple Interest = $4284

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 × 4284}/_{6800 × 7}

= ⁴²⁸⁴⁰⁰/₄₇₆₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $6800

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

Simple Interest = $4284 (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 $6800

= ⁷/₁₀₀ × 6800

= ^{7 × 6800}/₁₀₀

= ⁴⁷⁶⁰⁰/₁₀₀ = 476

Thus, simple Interest for 1 year = $476

Now,

∵ If the simple Interest is $476, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₆ years

∴ If the simple Interest is $4284, then the time = ¹/₄₇₆ × 4284 years

= ^{1 × 4284}/₄₇₆ years

= ⁴²⁸⁴/₄₇₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?

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

(4) Robert had to pay $3565 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?

(6) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.

(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.

(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?

(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.

(10) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.