Question

you would like to have $50,000 saved at the end of year 5. at the end of year 2, you can deposit $7,500 for this purpose. if you earn 4.5 percent, how much must you deposit today to reach your goal assuming no other deposits are made? group of answer choices $33,254.58 $33,108.09 $34,276.34 $34,642.28 $34,912.63

Answer 1

$33534.73 should be deposited today to reach the goal assuming on other deposits.

Let the lump sum be P.

The interest, I, on a rate, R%, per annum after T years is given by

                              I = PRT/100

The amount, A, is

      A = P + I = (1 + RT/100)

After 2 years at 4.5% interest rate, the amount is

A = P( 1 + 4.5 × 2 /100)

  = 1.09P

$7500 is added after 2 years. The principal for the beginning of the third year is then

                 1.09P + 7500

The amount after the next 3 years is

A = ( 1.09P + 7500) (1 + 4.5 ×3/100)

  = (1.09P + 7500) × 1.135

This is the amount expected to be saved.

5000 = (1.09P + 7500) × 1.135

Solving for P, we have

    1.09P + 7500 = 44052.86

⇒  1.09P = 36552.86

⇒ P = 33534.23

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