Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5700

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

Amount (A) = $9291

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 = $9291 – $5700 = $3591

Thus, Simple Interest = $3591

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 × 3591}/_{5700 × 7}

= ³⁵⁹¹⁰⁰/₃₉₉₀₀

= 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) = $5700

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

Simple Interest = $3591 (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 $5700

= ⁷/₁₀₀ × 5700

= ^{7 × 5700}/₁₀₀

= ³⁹⁹⁰⁰/₁₀₀ = 399

Thus, simple Interest for 1 year = $399

Now,

∵ If the simple Interest is $399, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₉ years

∴ If the simple Interest is $3591, then the time = ¹/₃₉₉ × 3591 years

= ^{1 × 3591}/₃₉₉ years

= ³⁵⁹¹/₃₉₉ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?

(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.

(3) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

(4) How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?

(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?

(6) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?

(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.

(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?

(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?

(10) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.