A. How much should you invest each month in order to have $800,000 if your rate of return is 5.3% compounded monthly and you want to achieve your goal in 40 years?
B. How much interest will you earn?
C. If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?
What instrument are you using: annuity, bonds, savings account? Different instruments earn in different ways.
annuity
To solve these questions, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value of the investment
P is the principal (initial investment)
r is the annual interest rate (in decimal form)
n is the number of times the interest is compounded per year
t is the number of years
A. How much should you invest each month in order to have $800,000 if your rate of return is 5.3% compounded monthly and you want to achieve your goal in 40 years?
To determine the monthly investment amount, we can rearrange the formula as follows:
P = A / (1 + r/n)^(nt)
Substituting the given values:
A = $800,000
r = 5.3% = 0.053 (decimal form)
n = 12 (compounded monthly)
t = 40 years
P = $800,000 / (1 + 0.053/12)^(12*40)
Now we can calculate this using a calculator or spreadsheet. The result will be the monthly investment amount you need to make.
B. How much interest will you earn?
The interest earned can be calculated by subtracting the principal amount from the future value.
Interest = A - P
Substituting the given values:
A = $800,000 (future value from the previous question)
P = Monthly investment amount calculated from the previous question
The result will be the total interest earned over the 40-year period.
C. If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?
To calculate the future value after 10 years with a 5.3% annual interest rate compounded monthly, we use the formula:
A = P(1 + r/n)^(nt)
Substituting the given values:
P = Amount needed to achieve goal in 20 years (calculated using a similar process as in question A)
r = 5.3% = 0.053 (decimal form)
n = 12 (compounded monthly)
t = 10 years
Now we can calculate A using a calculator or spreadsheet. The result will be the savings amount after 10 years.