Question

You would like to have $50,000 in 15 years. To accumulate this amount, you plan to deposit an equal sum in the bank each year that will earn 7% interest compounded annually. Your first payment will be made at the end of the year.

How much must you deposit annually to accumulate this amount?

(b) If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should this lump-sum deposit be? (Assume you can earn 7% annual interest on this deposit.) (

c) At the end of five years, you will receive $10,000 and deposit this in the bank toward your goal of $50,000 at the end of 15 years. In addition to this deposit, how much must you deposit in equal annual deposits to reach your goal? 1206.91(Again, assume you can earn 7% annual interest on this deposit.)

Answer 1

(a)

Compute the annual amount using the equation as shown below:

Accumulated amount = Annual amount * [(1 + Rate)^(Period) - 1 ] / Rate

$50,000 = Annual amount * [(1 + 7%)^(15) - 1] / 7%

$50,000 = Annual amount * 25.12902201

Annual amount = $50,000 / 25.12902201

= $1,989.731235

Hence, the annual amount is $1,989.73125.

(b)

Compute the large-lump sum deposit using the equation as shown below:

Accumulated amount = Lump sum amount * ( 1 + Rate) ^ (Period)

$50,000 = Lump sum amount * ( 1 + 7%) ^(15)

Lump sum amoumt = $50,000 / ( 1 + 7%) ^ 15

= $18,1222.30098

Hence, the lump sum amount is $18,122.30098.

(c)

Compute the annual amount using the equation as shown below:

Accumulated amount = [Annual amount * [(1 + Rate)^(Period) - 1 ] / Rate] + Depost * ( 1 + Rate) ^ (Total period - 5)

$50,000 =  [Annual amount * [(1 + 7%)^(15) - 1] / 7%] + $10,000 * ( 1 + 7%) ^(15-5)

= Annual amount * 25.12902201 + $10,000 * ( 1 + 7%) ^10

= Annual amount * 25.12902201 + $19,671.51357

Annual amount = ($50,000 - $19,671.51537) / 25.12902201

= $1,206.91

Hence, annual amount is $1,206.91.