Question - Calculating Present Value for Compound Interest Investment
mathannual interest rateinvestment growthpresent value formulacompound interest investmentcalculate present value
Solution:
To determine the present value required for an investment to grow to a future amount, we will use the present value formula for compound interest:$$ PV = \frac{FV}{{(1 + r/n)}^{(nt)}} $$where:- PV = present value (the amount to be invested now)- FV = future value (the desired accumulated amount)- r = annual interest rate (as a decimal)- n = number of times the interest is compounded per year- t = number of years the money is investedGiven information:- FV = $110,000- r = 2% or 0.02 (as a decimal)- n = 4 (since the interest is compounded quarterly)- t = 4 yearsPlugging these values into the formula gives us the present value:$$ PV = \frac{110,000}{{(1 + 0.02/4)}^{(4*4)}} $$$$ PV = \frac{110,000}{{(1 + 0.005)}^{16}} $$$$ PV = \frac{110,000}{{1.005}^{16}} $$Now we will calculate $$1.005^{16}$$ and then divide 110,000 by this result:$$ 1.005^{16} = 1.082856 $$ (rounded to six decimal places)So,$$ PV = \frac{110,000}{1.082856} $$$$ PV ≈ 101,576.65 $$Therefore, the amount to be invested now, or the present value needed, is approximately $101,576.65.
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