Question

Plz using Mathematical Fomulars to sovle questions as followed:

You would like to have $75,000 in 15 years. To accumulate this amount, you plan to deposit an equal sum in the bank each year that will earn 8 percent interest compounded annually. Your first payment will be made at the end of the year.

a. 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 the lump-sum deposit be? (Assume you can earn 8 percent on this deposit.)

c. At the end of five years, you will receive $20,000 and deposit it in the bank in an effort to reach your goal of $75,000 at the end of 15 years. In addition to the deposit, how large must your equal annual deposits for all 15 years be to reach your goal? (Again, assume you can earn 8 percent on this deposit.)

Answer 1

a. How much must you deposit annually to accumulate this amount?

We are given the following information:

Annual payment	PMT	To be calculated
rate of interest	r	8.00%
number of years	n	15
Required future value	FV	$            75,000.00

We need to solve the following equation to arrive at the required PMT

So the annual payment required is 2762.22

b. We are given the following information:

Lump sum need to be deposited now	PV	To be calculated
rate of interest	r	8.00%
number of years	n	15
Required future value	FV	$            75,000.00

We need to solve the following equation to arrive at the required PV

So the lump sum required right now is23643.13

c. As there will be a deposit of 20000 at the end of 5 years the we need to compound it for 10 years, subtract its FV from the 75000 and then we need to find the annual payment for the balance FV.

We are given the following information

Lump sum need to be deposited now	PV	20000
rate of interest	r	8.00%
number of years	n	10
future value	FV	To be calculated

We need to solve the following equation to arrive at the required FV

So the deposit of 20000 will become 43178.50 and so the required amount from annual payments is 75000-43178.50 =  $31,821.50

Now this is the required FV so accordingly we need to calculate the annual payment.

We are given the following information

Annual payment	PMT	To be calculated
rate of interest	r	8.00%
number of years	n	15
Required future value	FV	$            31,821.50

We need to solve the following equation to arrive at the required PMT

So the Annual payment required is 1171.97