Simple Interest
Math MCQs

Question :    In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3050

Rate of Simple Interest (R) = 3% per annum

Amount (A) = $3416

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 = $3416 – $3050 = $366

Thus, Simple Interest = $366

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 × 366}/_{3050 × 3}

= ³⁶⁶⁰⁰/₉₁₅₀

= 4 years (using formula)

Thus, Time (T) = 4 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) = $3050

Rate of Simple Interest (R) = 3% per annum

Simple Interest = $366 (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 = 3% of Principal

= 3% of $3050

= ³/₁₀₀ × 3050

= ^{3 × 3050}/₁₀₀

= ⁹¹⁵⁰/₁₀₀ = 91.5

Thus, simple Interest for 1 year = $91.5

Now,

∵ If the simple Interest is $91.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/_91.5 years

∴ If the simple Interest is $366, then the time = ¹/_91.5 × 366 years

= ^{1 × 366}/_91.5 years

= ³⁶⁶/_91.5 = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if James borrowed a sum of $3000 at a 7% simple interest?

(3) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.

(5) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?

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

(8) What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?

(9) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?

(10) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7208 to clear the loan, then find the time period of the loan.