Question

How do you find the present value that will grow to $30,000 if interest is 6% compounded quarterly for 11 quarters?

Answer 1

Hint: The given question is about getting the present value for the given set of conditions for according to the question given, here in order to solve the question we need to use the formulae for the fixed value in respect of present value with the time period and the rate of increment or decrement, and by putting the values in the formulae we can get the answer for the question.

Complete step-by-step answer:
For the given question we are going to use the respective formulae for getting the solution of the problem, here we are having the relation within the fixed value, present value, time period and the rate of interest; here we are going to use the formulae as:
 \[ \Rightarrow FV = PV{(1 + R)^T}\]
Here,
FV=Fixed price
PV=Present value
R=Rate of interest
T= Time period
Now finding the rate of interest we get;
 \[ \Rightarrow R = \dfrac{6}{{400}} = 0.015\]
Here R is calculated by changing the give rate of interest from percentage to value, and four is divided because it is given for the quarters instead of annual rate of interest.
Now using formulae we get:
 \[
   \Rightarrow FV = PV{(1 + R)^T} \\
   \Rightarrow 30000 = PV{(1 + 0.015)^{11}} \\
   \Rightarrow PV = \dfrac{{30000}}{{{{(1 + 0.015)}^{11}}}} = \dfrac{{30000}}{{{{1.015}^{11}}}} = 25468 \;
 \]
Hence we got the value of the present value for the given question.
So, the correct answer is “25468”.

Note: Here in order to solve the question we need to solve the question by using the formulae given with the associated question, without acknowledging with the formulae we cannot solve the given situation, in the question.