We are going to invest 100000 in an account that cams intere

We are going to invest $100,000 in an account that cams interest at a rate of 7.5% for 54 months. Determine how much money will be in the account if, interest is compounded quarterly. interest is compounded monthly. interest is compounded continuously. We are going to put $2500 into an account that earns interest at a rate of 12%. If we want to have $4000 in the account when we close it how long should we keep the money in the account if, we compound interest continuously. we compound interest 6 times a year

Solution

Dear Student,

You have posted 2 different questions.I will answer Question 1 to explain the concept.

The subsections of 1st question are:

A) Interest is compounded quarterly: In a compound interest problem, this means that in every 3 months, the interest is to be applied on the initial amount that was invested. We know that the monthly interest rate is 7.5 divided by 12 as given in the problem ( by default, if an interest rate is given it is considered for 12 months i.e anually). Thus it is 0.625% monthly. Therefore, for 1 quarter i.e 3 months, it will be 3 times 0.625 i.e 1.875%

Therefore, using the compound interest formula, the future value of money will be given by PV*(1+R)^n

where PV=$100,000 ,R=1.875% and n is the number of interest deposits that we are going to receive. As per the question, in 54 months we will be receiving 54/3 i.e 18 interest deposits in total.

Thus FV=100000*(1+1.875/100)^18 =$139,706.68

B) This should be easy by now, this is monthly and therefore FV=100000*(1+0.625/100)^54 , Here n=54 because the interest will be calculated 54 times for each of the 54 months.

therefore answer is $139996.84

Did you note that this value is greater than the previous answer. Why? because we are calculating the interest more number of times in this scenario :) 54 vs 18 times in previous question

c) For continuous interest calculation, just remember this formula:

We are talking about 54 months. i.e 54/12 years Also, r here is 7.5%

Therefore, A=100,000*(e^(7.5*54/1200))=140143.96 See that this is maximum out of other two answers. Here it is an exponential growth of our amount.

I hope it was helpful! Cheers :)