A woman would like to open a store in 8 years. She figures she will need 50,000 in capital to do so. She will make 10% on her money.
a. How much would she need to invest today in one lump sum to end up with 50000 in 8 years?
I got 23,325.25
b. if she's starting from scratch how much would she have to put away annually to accuulate the needed capital in 8 years?
I got 1247.82
c. how about if she already has 10,000 put away, how much would she have to put away to accumulate the needed capital in 8 years?
--This is the one I am stuck on. Also check my previous answers, they seem right but IDK. Thanks for any input!
a. P = Po + Po*r*t.
Po + Po*0.10*8 = $50,000.
Po + 0.8Po = 50,000.
1.8Po = 50,000.
Po = 50,000 / 1.8 = $27,777.78.
answer to c. If you expect to earn a 10.000% interest rate, compounded annually, you will need to deposit/invest $18,660.30 now in order for your investment to grow to $40,000.00 over the course of the next 8 years.
To calculate the answer to question c, we can break it down into two parts.
First, let's determine the amount she needs to invest if she already has $10,000 put away. The total capital required is still $50,000, but she already has $10,000, so she needs an additional $40,000.
Now, let's calculate how much she would have to put away annually to accumulate $40,000 in 8 years. We can use the future value of an ordinary annuity formula:
FV = P * ( (1 + r)^n - 1 ) / r
Where:
FV = future value (target amount of $40,000)
P = periodic payment (what she needs to put away annually)
r = interest rate per compounding period (10% or 0.10)
n = number of compounding periods (8 years)
Plugging in the values, we get:
40,000 = P * ( (1 + 0.10)^8 - 1 ) / 0.10
Now we can solve for P:
P = 40,000 * 0.10 / ( (1.10)^8 - 1 )
Calculating this, we find that she would need to put away approximately $3,689.19 annually to accumulate the remaining $40,000 in 8 years.
Therefore, if she already has $10,000 put away, she would need to put away an additional $3,689.19 annually to accumulate the needed capital of $50,000 in 8 years.