Question

Miss. Mulán wants to have money available for two trips he wants to make within two (2) and (four) 4 years respectively. For the first trip (year 2), it will require $ 50,000 MN and for the second (year 4) of $ 65,000 MN. Therefore he knows that he must save. The bank that offers the best interest rate is the ACME bank with an annual compound interest rate of 4.5%. How much should you deposit today in order to have the amounts you want in the years that your trips are scheduled?

Answer 1

To solve this question , we must know that

If an amound A is deposited

Annual compound intrest = R%.

Then , Amount he would have at the end of n years =

We need an amound of $50,000 in 2 years , $ 65,000 in 4 years.

we will find the principal amount required for both the trips seperately and add them to get the total amount he needs to deposit in the bank.

First Trip :-

Let , A1 be the amound deposited.

Rate of intrest = 4.5%.

Number of years = 2.

We need to find the amount A₁ that has to be invested in the bank , so that we get $50,000 after 2 years.

So , $50,000 =

From the above equation , A_{1 =}

₌ $ 45,786.49756

Second Trip :-

Let A₂ be the amount deposited.

Rate of Intrest = 4.5%

Number of Years = 4.

We are trying to find the amount A₂ that has to be invested , so that we can afford the second trip.

SO , $65,000 =

From the above equation , A₂ =

= $ 54,506.48733

The Total amount A that has to be deposited ,so that Miss.Mulan can go for both the trips = A₁ + A₂

  A = A₁ + A₂

= 45,786.49756 + 54,506.48733

= $ 100,292.9849

SOo , $100,292.9849 should be deposited today to have the amounts required for both the trips.

I hope that , it helps.If you have any queries regarding the solution , put it in the comments . I will modify / edit the answer according to your needs. Have a nice day :)