Simple Interest
Math MCQs

Question :    Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5300

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $8268

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 = $8268 – $5300 = $2968

Thus, Simple Interest = $2968

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 × 2968}/_{5300 × 8}

= ²⁹⁶⁸⁰⁰/₄₂₄₀₀

= 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) = $5300

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $2968 (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 = 8% of Principal

= 8% of $5300

= ⁸/₁₀₀ × 5300

= ^{8 × 5300}/₁₀₀

= ⁴²⁴⁰⁰/₁₀₀ = 424

Thus, simple Interest for 1 year = $424

Now,

∵ If the simple Interest is $424, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₄ years

∴ If the simple Interest is $2968, then the time = ¹/₄₂₄ × 2968 years

= ^{1 × 2968}/₄₂₄ years

= ²⁹⁶⁸/₄₂₄ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(2) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?

(3) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.

(4) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.

(5) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?

(7) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.

(9) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?

(10) How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?