Answer:
To find the periodic deposit investment amounts, we need to use the future value formula for each compounding period with the given future value, interest rate, and time.
The future value formula is:
FV = PMT * [(1 + r/n)^(n*t) - 1] / (r/n)
Where:
FV = Future Value
PMT = Periodic Deposit Amount (to be calculated)
r = Annual Interest Rate
n = Number of Compounding Periods per Year
t = Time in Years
a. For $50,000 future value, 2% compounded annually for 8 years:
n = 1 (annually)
50,000 = PMT * [(1 + 0.02/1)^(1*8) - 1] / (0.02/1)
PMT = $5,512.22
b. For $25,000 future value, 1.5% compounded semiannually for 4 years:
n = 2 (semiannually)
25,000 = PMT * [(1 + 0.015/2)^(2*4) - 1] / (0.015/2)
PMT = $5,645.33
c. For $100,000 future value, 1.25% compounded quarterly for 10 years:
n = 4 (quarterly)
100,000 = PMT * [(1 + 0.0125/4)^(4*10) - 1] / (0.0125/4)
PMT = $8,189.59
d. For $1,000,000 future value, 0.94% compounded monthly for 20 years:
n = 12 (monthly)
1,000,000 = PMT * [(1 + 0.0094/12)^(12*20) - 1] / (0.0094/12)
PMT = $2,794.48
Please ensure to format the answers with dollar signs ($) and use proper rounding as instructed.
