What is the present value of $6,700 received 14 years from now using an 11% interest rate, compounded quarterly?

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To find the present value of $6,700 received 14 years from now with an interest rate of 11% compounded quarterly, we need to apply the present value formula for compound interest.

The formula for present value (PV) is:

[ PV = \frac{FV}{(1 + r/n)^{nt}} ]

Where:

(FV) is the future value ($6,700 in this case).
(r) is the annual interest rate (0.11 for 11%).
(n) is the number of times interest is compounded per year (4 for quarterly).
(t) is the number of years (14 years).

Plugging in the values:

Convert the interest rate to a quarterly rate: ( r/n = 0.11 / 4 = 0.0275 ).
Calculate the total number of compounding periods: ( nt = 4 \times 14 = 56 ).
Substitute the values into the formula: [ PV = \frac{6700}{(1 + 0.0275)^{56}} ] [ PV = \frac{6700}{(1