Final answer:
To have $10,000 in 7 years at a 5% interest rate compounded quarterly, one must invest approximately $7057.95 today.
Step-by-step explanation:
The question asks: How much must be invested now at a nominal rate of 5% in order to have $10,000 in 7 years' time if interest is compounded quarterly? To address this issue, we can employ the compound interest formula: A = P(1 + r/n)^(nt), wherein:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the nominal rate (annual interest rate).
- t is the time in years.
- n represents the frequency at which interest is compounded annually.
In this case, A is $10,000, r is 0.05 (5% written as a decimal), t is 7 years, and n is 4 (since interest is compounded quarterly).
Plugging these values into the formula gives us:
10000 = P(1 + 0.05/4)^(4*7)
Now solve for P:
P = 10000 / (1 + 0.05/4)^(4*7)
P = 10000 / (1.0125)^28
P = 10000 / 1.416080
P ≈ $7057.95
Therefore, about $7057.95 must be invested today to have $10,000 in 7 years when the interest is compounded quarterly.