Simple Interest
Math MCQs

Question :    Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5300

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

Amount (A) = $7526

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 = $7526 – $5300 = $2226

Thus, Simple Interest = $2226

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 × 2226}/_{5300 × 7}

= ²²²⁶⁰⁰/₃₇₁₀₀

= 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) = $5300

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

Simple Interest = $2226 (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 $5300

= ⁷/₁₀₀ × 5300

= ^{7 × 5300}/₁₀₀

= ³⁷¹⁰⁰/₁₀₀ = 371

Thus, simple Interest for 1 year = $371

Now,

∵ If the simple Interest is $371, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₇₁ years

∴ If the simple Interest is $2226, then the time = ¹/₃₇₁ × 2226 years

= ^{1 × 2226}/₃₇₁ years

= ²²²⁶/₃₇₁ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?

(4) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?

(5) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) How much loan did Donna borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8562.5 to clear it?

(7) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

(8) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 3 years.

(10) 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.