# You expect to receive \$29,000 at graduation in two years. You plan on investing it at 10 percent until you have \$164,000.how long it takes?

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• Anonymous
5 months ago

Yes I have spoken to her and I met her. It is love.

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• Good luck in finding somewhere that pays 10%. This must be a really old question.

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• Why would I receive \$29,000 when that could be used to pay off the tuition

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• Compound Interest:

A(t) = A₀(1 + r/n)^(nt)

A(t) = compounded amount after t years = 164000

A₀ = original amount = 29000

r = annualized rate of interest = 0.10

n = number of compounding periods per year

t = number of years.

164000 = 29000(1+0.10/n)^(nt)

164/29 = (1+0.10/n)^(nt)

log(164/29) = (nt)log(1+0.10/n)

t = log(164/29)/[n log(1+0.10/n)

Annual Compounding: n = 1

t = log(164/29)/log(1.1) ≈ 18.2 → 19 years

Monthly Compounding: n = 12

t = log(164/29)/[12log(1+1/120)] ≈ 17.4 → 18 years

Daily Compounding : n = 360 [Financial calculations commonly use 30 days per month, 360 days per year]

t = log(164/29)/[360log(1+1/3600)] ≈ 17.3 → 18 years

Continuous Compounding: A(t) = A₀e^(rt)

t = ln(164/29)/0.1 ≈ 17.3 → 18 years

Simple Interest: A(t) = A₀(1+rt)

t = [(164/29) - 1]/0.10 = 46.6 → 47 years

Depending on the tax implications of the type of investment, you may be required to pay income taxes on the annual increase in the value of the investment which may appreciably extend the time before the net worth of the investment reaches \$164000.

Ans:

Depending on the type of return, it will take somewhere between 18 and 47 years if you can reliably achieve a rate of return of 10% over the entire term.

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• Please tell me where I can invest in a guarantee of 10% return?

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• 164000 = 29000 * 1.1^x

164/29 = 1.1^x

ln(164/29) = x * ln(1.1)

ln(164/29) / ln(1.1) = x

x = ‭18.178232392329471658122857026259‬....

18.18 years, roughly, just round up to 19 years.

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