Question 1 Our parents have $250,000 in savings now, but they want $1,000,000 wh

Question

Question 1 Our parents have $250,000 in savings now, but they want $1,000,000 when they retire in 18 years. What interest rate must they earn on their current savings to get to their retirement goal? Question 2 We have $42,180.53 right now, but we want $250,000. We can deposit $5000 annually, and we can get a 12% annual return. How long will it take to get to our financial goal? Question 1 Our parents have $250,000 in savings now, but they want $1,000,000 when they retire in 18 years. What interest rate must they earn on their current savings to get to their retirement goal? Question 2 We have $42,180.53 right now, but we want $250,000. We can deposit $5000 annually, and we can get a 12% annual return. How long will it take to get to our financial goal?

Explanation / Answer

Answer 1:

The formula for annual compound interest is A = P (1 + r/n) ^ nt:

Where:

A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for

A= $1,000,000

P= $250,000

R= R

n= 1

   t=18   

1,000,000 = 250,000(1+r)^18

4=(1+r)^18

1 + i = (4)1/18

          i = 1.08 - 1 = 0.08 or 8%

          The required rate of interest to reach the goal is 8%.

Solve for r using scientific calculator it comes to 8.01%

Answer 2:

Present value (PV) = $ 42,180.53

             Payment (PMT) = $ 5,000

             Annual return (i) = 12%

             Future value (FV) = $ 250,000

             Number of years to reach goal (n) = ?

                     

We have,

             $ 42,180.53 (1 + 0.12)n + $ 5,000 = $ 250,000

             or,    5,061.66 (1.12)n + $ 5,000 (1.12)n - $ 5,000 = $ 30,000

             or,    10,061.66 (1.12)n = $ 35,000

             or,    (1.12)n = £ 35,000/ $ 10,061.66

             or,    (1.12)n = 3.4786                ... (i)

             In above eqn. (i) if we go for trying several values of 'n', the left hand side is exactly equal to right hand side at n = 11.

         The required no. of years to reach the goal is 11 years.

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