Question

You would like to save $ 2000 for a trip at the end of your degree in three years. You deposit $15,00 today and will make another deposit in 18 months. How much should you deposit so that you will have 2000 in three years if you will earn 3% simple? Use three years as your focal date.

Answer 1

Interest wil be received on $1500 for three years.

So Interest on 1500 for 3 years at rate 3% simple interest.

Interest= P*R*T

P = Principal

R = Rate of Interest

T = Time/ Number of years

Putting values in formula,

Interest = 1500 * 3% * 3

= 135

Total amount including Interest amd principal= 1500 + 135 ==> 1635.

Now, maturity amount needed is $ 2000 after 3 years.

We have to calculate the amount to be deposited in 18 months that is 1.5 year to get $2000.

So,

Let 'x' be the amount to be deposited after 18 months.

Maturity amount = Amount already deposited including interest for 3 years + Amount to be deposited after 18 months + Interest on amount to be deposited after 18 months ( Amount to be deposited after 18 months * 3% * 1.5)

2000 = 1635 + x + (x * 3% * 1.5)

365 = x + 0.045 x

365 = 1.045 x

x = 349.28

x ~ 350

Amount to be deposited after 18 months= $350

Can be calculated this way also :

Let amount to be deposited after 18 months (1.5 year) be 'x'.

Maturity amount = (Principal of 1500+ Interest on 1500 for 1.5 years)+ ( Amount to be deposited + Interest on 1500 and amount to be deposited for 1.5 year)

2000 = [1500 + (1500 * 3% * 1.5)] + [x + ( 1500 + x) * 3% * 1.5]

2000 = (1500 + 67.5) + [x + ( 1500 + x ) * 0.045]

2000 = 1567.5 + ( x + 67.5 + 0.045x)

365 = x + 0.045x

365 = 1.045 x

x = 349.28

x~ 350