1. How much will $800 deposited into a savings account at the end of each month be worth after 2 years at 6% interest compounded monthly?
2. How much will $3,500 deposited at the beginning of each 3-month period be worth after 7 years at 12% interest compounded quarterly?
3. What amount must be deposited now to withdraw $200 at the beginning of each month for 3 years if interest is 12% compounded monthly?
4. How much must be deposited now to withdraw $4,000 at the end of each year for 20 years if interest is 7% compounded annually?
For each of these problems, just solve for A or P, using the formula
A = P(1 + r/n)^(nt)
where n is the number of times compounded in a year, and r is the interest rate (as a decimal ... 5% = 0.05)
How much will $8000 deposited into a savings account at the end of each month be worth after 2 years at 6% interest compounded monthly?
1. To calculate the worth of $800 deposited into a savings account at the end of each month after 2 years at 6% interest compounded monthly, you can use the formula for compound interest:
Future Value = P * (1 + r/n)^(n*t)
where,
P = Principal amount ($800)
r = Annual interest rate (6% or 0.06)
n = Number of compounding periods in a year (12 since it's compounded monthly)
t = Number of years (2)
Substituting the values into the formula:
Future Value = 800 * (1 + 0.06/12)^(12*2)
Now, you can use a calculator or a spreadsheet software to compute the result. The future value will be the worth of the $800 deposits after 2 years at 6% interest compounded monthly.
2. To find out how much $3,500 deposited at the beginning of each 3-month period will be worth after 7 years at 12% interest compounded quarterly, you can use the same formula as before:
Future Value = P * (1 + r/n)^(n*t)
In this case,
P = Principal amount ($3,500)
r = Annual interest rate (12% or 0.12)
n = Number of compounding periods in a year (4 since it's compounded quarterly)
t = Number of years (7)
Substituting the values:
Future Value = 3500 * (1 + 0.12/4)^(4*7)
Again, you can use a calculator or a spreadsheet to compute the result. The future value will be the worth of the $3,500 deposits after 7 years at 12% interest compounded quarterly.
3. To determine the amount that must be deposited now to withdraw $200 at the beginning of each month for 3 years with an interest rate of 12% compounded monthly, you can use the formula for present value of an annuity:
Present Value = P * ((1 - (1 + r/n)^(-n*t)) / (r/n))
Here,
P = Payment amount ($200)
r = Annual interest rate (12% or 0.12)
n = Number of compounding periods in a year (12 since it's compounded monthly)
t = Number of years (3)
Substituting the values:
Present Value = 200 * ((1 - (1 + 0.12/12)^(-12*3)) / (0.12/12))
Once again, you can use a calculator or a spreadsheet to compute the result. The present value will be the amount that needs to be deposited now to withdraw $200 at the beginning of each month for 3 years at 12% interest compounded monthly.
4. To calculate the amount that must be deposited now to withdraw $4,000 at the end of each year for 20 years at an interest rate of 7% compounded annually, you can use the formula for present value of an annuity:
Present Value = P * (1 - (1 + r/n)^(-n*t)) / (r/n)
In this case,
P = Payment amount ($4,000)
r = Annual interest rate (7% or 0.07)
n = Number of compounding periods in a year (1 since it's compounded annually)
t = Number of years (20)
Substituting the values:
Present Value = 4000 * (1 - (1 + 0.07/1)^(-1*20)) / (0.07/1)
Once again, use a calculator or a spreadsheet to calculate the result. The present value will be the amount that needs to be deposited now to withdraw $4,000 at the end of each year for 20 years at 7% interest compounded annually.