Question

A fund starts with a zero balance at time zero. The fund accumulates with a varying force of interest : δ t = 2 t t 2 + 1 for t > 0 A deposit of $100,000 is made at time 2. Calculate the number of years from the time of deposit for the fund to double.

Answer 1

Answer and Explanation:

Given function

S(t) =2t/t²+1 where t > 0

and fund accumulates with a varying force of interest.

and $100,000 is deposited at time 2.

Number of years it will take from the time of deposit for the fund to double,

Substituting t in the formula given that t is 1 because t>0 and deposit begins to grow from time of deposit 2

= S(t)= 2*1/1² + 1=1

Therefore time it will take for funds to double is 1 year from time of deposit