Final answer:
To find out how much a company needs to invest now to have $3.5 million in 8 years with 7% interest compounded monthly, you must use the present value formula accounting for compound interest.
Step-by-step explanation:
To calculate how much the company needs to invest now to have $3.5 million in 8 years with an interest rate of 7% compounded monthly, we will use the formula for the present value of a future amount when compounded at a regular interval:
PV = FV / (1 + r/n)nt
Where:
- PV = Present Value (amount to invest now)
- FV = Future Value ($3.5 million)
- r = annual interest rate (7% or 0.07)
- n = number of times interest is compounded per year (12 for monthly)
- t = number of years (8)
Substituting these values:
PV = 3,500,000 / (1 + 0.07/12)12*8
Now you calculate the denominator:
(1 + 0.07/12)96
And then divide the future value by this amount to find the present value.
The company must invest this present value amount in the account to meet the future obligation of $3.5 million.
It is important to understand that compound interest can significantly increase the future value, especially over a long period. Unlike simple interest, which only applies to the principal amount, compound interest takes into account the accumulated interest over time as well.