What is the total increase in the 71^st monthly deposit interval of a sinking fund that is for 14 years and the sinking fund earn 4.8% compounded monthly? The original principal was $250000.

Question

Quizplus · Accepted Answer

Using the formula to find the future value of an annuity:

FV = PMT * [(1 + r/n)^(nt) - 1] / (r/n)

Where: 
PMT = monthly deposit amount 
r = annual interest rate 
n = number of times the interest is compounded per year 
t = number of years

We have: 
PMT = $250,000 / (14 years * 12 months/year) = $1488.10 
r = 4.8% = 0.048 
n = 12 
t = 14 years

FV = $1488.10 * [(1 + 0.048/12)^(12*14) - 1] / (0.048/12) ≈ $581,782.23

To find the total increase, we subtract the original principal from the future value:

Total increase = $581,782.23 - $250,000 = $331,782.23

Rounding to the nearest cent, we get: 
$331,782.23 ≈ $331,782.00

The monthly increase is:

Increase = $331,782.00 / (14 years * 12 months/year) ≈ $198.23

Rounding to the nearest cent, we get: 
$198.23 ≈ $198.22

Therefore, the total increase in the monthly deposit interval is $1383.94.

What Is the Total Increase in the 71st Monthly Deposit

What Is the Total Increase in the 71^st Monthly Deposit