Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5600

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $7952

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 = $7952 – $5600 = $2352

Thus, Simple Interest = $2352

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 × 2352}/_{5600 × 6}

= ²³⁵²⁰⁰/₃₃₆₀₀

= 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) = $5600

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2352 (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 = 6% of Principal

= 6% of $5600

= ⁶/₁₀₀ × 5600

= ^{6 × 5600}/₁₀₀

= ³³⁶⁰⁰/₁₀₀ = 336

Thus, simple Interest for 1 year = $336

Now,

∵ If the simple Interest is $336, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₃₆ years

∴ If the simple Interest is $2352, then the time = ¹/₃₃₆ × 2352 years

= ^{1 × 2352}/₃₃₆ years

= ²³⁵²/₃₃₆ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.

(2) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.

(3) If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?

(5) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.

(6) If Elizabeth paid $4002 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.

(9) If Linda borrowed $3350 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 4% simple interest?