Question

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How much money will be in an account in 5 years if $10,000 is deposited now at an interest rate of 1% per month? Use three different interest rates: (a) monthly, (b) quarterly , and (c) yearly. (a) For monthly rate, 1% is effective [n= (5 years)x(12 CP per year = 60] F = 10,000(F/2,1%,60) = $18,167 months % i and n must always have effective i per month J same time units (b) For a quarterly rate, effective i/quarter = (1 + 0.03/3)3 – 1 = 3.03%F= 10,000(F/2,3,03%,20) = $18,167 i and n must always have effective i per quarter - same time units (c) For an annual rate, effective i/year = (1 + 0.12/12)12 – 1 = 12.683%F= 10,000(F/2,12.683%,5) = $18,167 i and n must always have effective i per year quarters years same time units

Answer 1

Formula for (F/P,i,n) = (1+i)^n

a.

per month interest rate = 1%

t = 5 * 12 = 60 months

Future worth = 10000 * (F/P,1%,60) = 10000 * (1+0.01)^60 = 10000 * 1.81669669 = 18166.97 ~ 18167 (Nearest Dollar)

b.

per month interest rate = 1%

Effective interest rate per quarter = (1+0.01)^3 - 1 = 1.0303 - 1 = 3.03%

t = 5 * 4 = 20 quarter

Future worth = 10000 * (F/P,3.03%,20) = 10000 * (1+0.0303)^20 = 10000 * 1.8166614 = 18166.61 ~ 18167 (Nearest Dollar)

c.

per month interest rate = 1%

Effective interest rate per quarter = (1+0.01)^12 - 1 = 1.126825 - 1 = 12.68%

t = 5 yrs

Future worth = 10000 * (F/P,12.68%,5) = 10000 * (1+0.1268)^5 = 10000 * 1.8166966 = 18166.96 ~ 18167 (Nearest Dollar)

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