Your company needs 400,000 dollars in two years time for renovations and can ear

Question

Your company needs 400,000 dollars in two years time for renovations and can earn 8% interest on investments.

a) What is the present value of the renovations?

Present value = ___________________________dollars

b) If your company deposits money continuously at a constant rate throughout the two-year period, at what rate should the money be deposited so that you have the 400,000 dollars when you need it?

Round your answers to 2 decimal places.

Money deposited at a rate of __________________________ dollars per year

Explanation / Answer

a) P = C (1 + r/n) nt   Variable meanings: (P=Final amount, C=Starting amount, r=rate, n=investments/year, (compound interest formula) t=years invested.)

400,000 = C(1+.08/1)(1*2)

400,000/(1.08)2 = C divide everything from C to solve for C

$342935.53 = C ----> Present value [Answer]

b) P = C e rt --------> New variable meaning: e=approx 2.7 (Used for calculating continuously deposited investments).

400,000 = 342935.53 e(r*2) ----> we don't know the rate, but we know the C = 34,2935.54 from part A.

400,000/342,935.53 = e(r*2) -----> divide the C value from both sides

ln(400,000/342,935.53) = r*2 -----> take the ln, which means natural log (this cancels e).

(ln(400,000/342,935.53))/2 = r ----> divide 2 from both sides

.08 = r or r = 8% --------> [Answer]

So the rate of the continuous deposit is equal to the rate of the yearly deposit for these

values (very common). I hope this helps!

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