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# Answer to Question #138145 in Finance for CH Tan

Question #138145
Angeline wishes to make six annual deposits in the amounts of $1,000,$2,000, $3,000,$4,000, $5,000 and$6,000, in that order, into a fund that pays interest at rate of 5% per
annum. Determine the value of amount today if
i) the interest is compounded annually
ii) the interest is compounded quarterly.
1
2020-10-15T03:00:56-0400

solution

Part i)

Compounding per annum

Rate "r=0.05"

Present value "PV = \\sum p_i(1+r)^{-i}"

"= \\frac{1000}{(1.05)^1} + \\frac{2000}{(1.05)^2} + \\frac{3000}{(1.05)^3}""+ \\frac{4000}{(1.05)^4} + \\frac{5000}{(1.05)^5} + \\frac{6000}{(1.05)^6}"

"= 17044.74"

answer: the present value is $17,044.74 Part ii) Compounding quarterly "PV = \\sum p_i(1+\\frac{r}{4})^{-i*4}" "= \\frac{1000}{(1.0125)^4} + \\frac{2000}{(1.0125)^8} + \\frac{3000}{(1.0125)^{12}}""+ \\frac{4000}{(1.0125)^{16}} + \\frac{5000}{(1.0125)^{20}} + \\frac{6000}{(1.0125)^{24}}" "=26116.03" answer: the present value is$ 26,116.03

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