# math

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A house is rented for \$2000 per quarter, with each quarter's rent payable in advance. If money is worth 2%, compounded quarterly, and the rent is deposited in an account, what is the future value of the rent for one year?

• math -

Assume 2% is per quarter (not per annum).
so R=1.02, n=4 quarters, and rent, P=\$2000.

Future value
P(R+R^2+R^3+R^4)
= PR(1+R+R^2+R^3)
=PR (R^4-1)/(R-1)
=2000*1.02*(1.02^4-1)/(1.02-1)
=\$8408.08

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