Question

NYC Equity Partners plans to accumulate $46,275,255 towards structuring a real estate investment trust by depositing $1,500,000 at the end of each year with JPMorgan. If Chicago Equity Partners earns 16% compounded annually on the deposited funds, how many deposits must it make?  

Answer 1

Given,

Future value = $46275255

Annual deposits (A) = $1500000

Interest rate (r) = 16% or 0.16

Solution :-

Let no. of deposits be 'n'

Future value = A/r x [(1 + r)ⁿ - 1]

$46275255 = $1500000/0.16 x [(1 + 0.16)ⁿ - 1]

$46275255 x 0.16/$1500000 = (1.16)ⁿ - 1

4.9360272 = (1.16)ⁿ - 1

4.9360272 + 1 = (1.16)ⁿ

5.9360272 = (1.16)ⁿ

Taking 'Log' both sides,

Log(5.9360272) = Log(1.16)ⁿ

Log(5.9360272) = n.Log(1.16)

1.7810400881 = n.(0.14842000512)

1.7810400881/0.14842000512 = n

12 = n

Thus, it must make 12 deposits.