Question

On June 1, 2020, a person needs $17700. The person will make equal monthly deposits to an account which earns 11% compounded monthly. If the first deposit is made on June 1, 2015 and the last deposit is made on May 1, 2020, find the size of the required monthly deposits (rounded up to the next cent) in order to have the $17700 on June 1, 2020.

Answer 1

The amount is computed as shown below:

Future value = Monthly deposits x [ [ (1 + r)ⁿ – 1 ] / r ]

r is computed as follows:

= 11% / 12 (Since the savings are monthly, hence divided by 12)

= 0.916666667% or 0.009166667

n is computed as follows:

= 7 months in 2015 + 12 months in 2016 + 12 months in 2017 + 12 months in 2018 + 12 months in 2019 + 4 months in 2020

= 59

So, the amount will be as follows:

$ 17,700 = Monthly deposits x [ [ (1 + 0.009166667)⁵⁹ - 1 ] / 0.009166667]

Monthly deposits = $ 227.4922

Now in order to get the amount on June 1, 2020, we need to multiply the above amount by (1 + r) as shown below:

= $ 227.4922 x 1.009166667

= $ 229.58 Approximately

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