You borrowed $50,000 which you must repay in 10 years. You plan to make an initial deposit today, then make 9 more deposits at the beginning of each the next 9 years, but with the deposits increasing at the inflation rate. You expect to earn 5% on your funds, and you expect a 3% inflation rate. To the nearest dollar, how large must your initial deposit be to enable you to reach your $50,000 target

$3,342

Explanation:

Given that,

Borrowed amount = $50,000

Repay in 10 years(n)

Required Rate of return = 5%

Inflation rate = 3%

Future value = $50,000

Real rate of return, r:

=

=

=

= 1.01941748 - 1

= 0.019417 or 1.9417%

Real future value:

=

=

=

= $37,204.69

Annual payment is calculated as follows:

=

=

= 3341.94 or 3,342 (Approx)

Therefore, the initial deposit must be $3,342 to reach your $50,000 target.

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