Diego contributes to a money market account that earns 4.8% annual interest. What should his monthly payment be if he wants to accumulate $210,000 in 30 years?
Thank you so much!!
Just plug your numbers into your FV annuity formula, and you get
P((1 + .048/12)^(12*30)-1) / ((1 + .048/12) - 1) = 210000
P = 261.80
To calculate the monthly payment Diego would need to make in order to accumulate $210,000 in 30 years with a 4.8% annual interest rate, we can use the formula for future value of an ordinary annuity.
The formula for future value of an ordinary annuity is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value of the annuity (desired accumulated amount)
P = Monthly payment
r = Monthly interest rate (annual interest rate / 12)
n = Number of periods (number of months in this case)
In this case, we want to accumulate $210,000 in 30 years. Since there are 12 months in a year, the number of periods would be 30 * 12 = 360 months.
First, we need to convert the annual interest rate to a monthly interest rate. To do that, we divide the annual interest rate by 12. Therefore, the monthly interest rate would be 4.8% / 12 = 0.48% (expressed as a decimal, 0.048).
Substituting the values into the formula:
$210,000 = P * [(1 + 0.048)^360 - 1] / 0.048
To solve for P, we need to rearrange the equation:
P = ($210,000 * 0.048) / [(1 + 0.048)^360 - 1]
Using a calculator, we can solve for P:
P ≈ ($210,000 * 0.048) / [(1.048)^360 - 1]
P ≈ ($10,080) / (5.1816 - 1)
P ≈ $10,080 / 4.1816
P ≈ $2,412.16
So, Diego should make a monthly payment of approximately $2,412.16 in order to accumulate $210,000 in 30 years with a 4.8% annual interest rate.