Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 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) = 6% per annum

Amount (A) = $8778

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 = $8778 – $5700 = $3078

Thus, Simple Interest = $3078

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 × 3078}/_{5700 × 6}

= ³⁰⁷⁸⁰⁰/₃₄₂₀₀

= 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) = 6% per annum

Simple Interest = $3078 (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 $5700

= ⁶/₁₀₀ × 5700

= ^{6 × 5700}/₁₀₀

= ³⁴²⁰⁰/₁₀₀ = 342

Thus, simple Interest for 1 year = $342

Now,

∵ If the simple Interest is $342, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₂ years

∴ If the simple Interest is $3078, then the time = ¹/₃₄₂ × 3078 years

= ^{1 × 3078}/₃₄₂ years

= ³⁰⁷⁸/₃₄₂ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?

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

(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?

(5) How much loan did Anthony borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7875 to clear it?

(6) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 3 years.

(7) How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?

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

(9) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.