You deposit $3,000 at the end of each quarter into an account that pays 9% interest compounded monthly. How much will be in the account after 5 years?
$91,415
$74,861
$71,177
$97,298
$85,978
$78,794
Amount deposited each quarter = P = $3000
Number of quarters = n = 5*4 = 20
Monthly Interest Rate = r = 0.09/12 = 0.0075
Hence, Future Value = FV = P(1+r)3n-3 +
P(1+r)3n-6 + .... + P(1+r)3 + P
Let (1+r)3 = 1 + x
=> FV = P(1+x)n-1 + P(1+x)n-2 + .... +
P(1+x) + P
= P[(1+x)n -1]/x
= P[(1+r)3n -1]/((1+r)3-1)
= 3000[(1+0.0075)60 -1]/((1+0.0075)3-1)
= $74,861
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