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savmoore savmoore
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5 years ago
HELP! What is the cash value of a lease requiring payments of ​$990 at the beginning of every three months three months for 77 ​years, if interest is 3 %3% compounded semi dash annually question mark semi-annually?
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Educator
5 years ago Edited: 5 years ago, bio_man
Quote from: savmoore (5 years ago)
HELP! What is the cash value of a lease requiring payments of $990 at the beginning of every three months three months for 77 years, if interest is 3 %3% compounded semi dash annually question mark semi-annually?

Use the formula for annuity.

\(A=\frac{R\left[\left(1+i\right)^n-1\right]}{i}\)

\(A\) = future value amount → what we're looking for!
\(R\) = regular deposit/payment → 990
\(i\) = interest rate per compounding period → 0.03/2 = 0.015
\(n\) = total number of deposits → 4 (every three months suggests four periods per year) * 77 = 308

\(A=\frac{990\left[\left(1+\frac{0.03}{2}\right)^{308}-1\right]}{\frac{0.03}{2}}=6 406 692.10\)

I arrive to this number: $6 406 692.10 (please double-check the calculation using your calculator!)
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