At age 5, how much would you have to save per month to have $1 million in your account at age 65, if your investment rate was 10% per year? Assume no taxes and compounding on a monthly basis.
$213.30
$21.23
$274.60
can't be done with these assumptions.
After 20 years, 100 shares of stock originally purchased for $1000 was sold for $5,000. What was the yield on the investment? Choose the closest answer.
19%
5%
12.7%
8%
Let x be the average yield, expressed as a decimal.
(1+x)^20 = 5000/1000 = 5
log 5 = 20 log(1+x)
log (1+x) = 0.0349585
1+x = 1.0837
x = 8.4%
8% is the closest answer
R = Si/[(1+i)^n - 1] where R = the monthly deposit, i = the periodic decimal interest rate, and n = the number of deposits.
R = 1,000,000
i = 10/100(12) = .008333
n = 60(12) = 720
R = 1,000,000(.008333)/[1.008333^720)-1]
R = 8333.333/(393.428 - 1)
R = $21.24
Check:
S = [1.008333^720 - 1]/.008333 = $1,000,262.
To calculate how much you would need to save per month to have $1 million in your account at age 65 with an investment rate of 10% per year, assuming no taxes and compounding on a monthly basis, you can use the formula for compound interest. The formula is:
A = P * (1 + r/n)^(n*t)
Where:
A = the future value of the investment (in this case, $1 million)
P = the principal amount (the amount you save per month)
r = the annual interest rate (10% or 0.10)
n = the number of times that interest is compounded per year (12, since interest is compounded monthly)
t = the number of years (65 - 5 = 60)
Simplifying the formula, we get:
1,000,000 = P * (1 + 0.10/12)^(12 * 60)
To find the value of P, we can rearrange the formula to solve for P:
P = 1,000,000 / (1 + 0.10/12)^(12 * 60)
Calculating this equation gives us an answer of approximately $213.30. Therefore, the correct answer to the first question is:
$213.30
Now let's move on to the second question. To calculate the yield on an investment, you can use the formula:
Yield = (Proceeds - Cost) / Cost
In this case, the proceeds from selling 100 shares of stock were $5,000, and the cost of purchasing the shares was $1,000. Plugging these values into the formula:
Yield = (5,000 - 1,000) / 1,000
Simplifying the equation gives us:
Yield = 4,000 / 1,000 = 4
Multiplying by 100 to convert to a percentage, the yield on the investment is 400%. However, since none of the given answer choices exactly match 400%, we should choose the closest option, which would be:
19%