Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8642 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5800

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

Amount (A) = $8642

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 = $8642 – $5800 = $2842

Thus, Simple Interest = $2842

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 × 2842}/_{5800 × 7}

= ²⁸⁴²⁰⁰/₄₀₆₀₀

= 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) = $5800

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

Simple Interest = $2842 (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 $5800

= ⁷/₁₀₀ × 5800

= ^{7 × 5800}/₁₀₀

= ⁴⁰⁶⁰⁰/₁₀₀ = 406

Thus, simple Interest for 1 year = $406

Now,

∵ If the simple Interest is $406, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₆ years

∴ If the simple Interest is $2842, then the time = ¹/₄₀₆ × 2842 years

= ^{1 × 2842}/₄₀₆ years

= ²⁸⁴²/₄₀₆ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?

(2) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 10% simple interest?

(4) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(5) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.

(6) How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?

(7) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?

(8) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?

(9) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?

(10) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.