Question

I would like to have $50,000 after retirement in 20 years 8 months from now. How much should I invest right now to reach my goal if interest rate remains the same for the next 30 years as 3% p.a.?

Answer 1

Solution.

As not specified in the question, we assume that simple interest is applied here.

we know for simple interest

  I = P x R x T

  where I = simple interest

p = principal amount invested initially

R = rate of interest (0.03 here)

T = time period for which we invested the amount (20 years 8 months here)

and A = P+I

A = final Amount (50,000 here)

  I = simple interest

p = principal amount invested initially

from     I = P x R x T   we can write  P = I/RT and

from A=P+ I, we can write I = A-P

now put the value of I in the above equation we get

P = (A -P) / RT

PRT =(A-P)

PRT +P =A

P(RT +1) =A

P = A / (RT+1)

now putting the values of A ,R, T in above equation ,

P = 50,000 / (0.03 x 20.667 + 1)

P = 50,000/ 0.620 +1

P = 50,000/ 1.620

P = 30,864.197  

Please note that for the value of T in question we have given 20 years and 8 months so we have converted the 8 months into year by doing (8/12) which is equal to 0.667 years approximately.