Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 7% 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  6

Solution & Explanation

Solution

Given,

Principal (P) = $5600

Rate of Simple Interest (R) = 7% 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 × 7}

= ²³⁵²⁰⁰/₃₉₂₀₀

= 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) = $5600

Rate of Simple Interest (R) = 7% 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 = 7% of Principal

= 7% of $5600

= ⁷/₁₀₀ × 5600

= ^{7 × 5600}/₁₀₀

= ³⁹²⁰⁰/₁₀₀ = 392

Thus, simple Interest for 1 year = $392

Now,

∵ If the simple Interest is $392, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₂ years

∴ If the simple Interest is $2352, then the time = ¹/₃₉₂ × 2352 years

= ^{1 × 2352}/₃₉₂ years

= ²³⁵²/₃₉₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

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

(3) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?

(4) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?

(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.

(7) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 2% simple interest?

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 3 years.

(9) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?

(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?