Question

3.         Lisa and David have been married for two years. They have just decided that summer of 2022 should be spent in Switzerland. They figured out that in order to meet the cost of the entire vacation they would only have to dedicate what they already have in their saving account now ($ 5,859.37) for that vacation, keeping their regular monthly saving during the next two years for different purposes. Given that the annual compound interest rate is 8.5%, how much would they be able to spend for their vacation?

4.         If the cost of vacation is $9,384.44, What would be the annual compound interest rate that would let their saving account accumulate to meet their vacation costs?

5.         How many years would they have to wait if the annual compound interest rate is 10%, the cost of vacation is $12,000, and their saving account now has only $7451.05 ?

Answer 1

Answer) We will use concept of compound interest to solve the questions,formula of amount generated at end of period using compound interest is as follows

Amount=Principal(1+interest rate)^no. of periods (note- since compounding is done annually we don't have to deal with no. of times in a period compounding has to be done in this question)

3.) Since couple already has savings equal to trip,any interest they earn on this savings now will be their spending power for vacation,principal or initial amount is $5,859.37 compound interest is 8.5% or 8.5/100=0.085,time period is 2 years (2022-2020) putting this in formula above we get

Amount=5859.37(1+0.085)^2=$6897.796

Now subtracting principal from this we get the amount they can spend on vacation which is

$6897.796-$5859.37=$1038.426

Thus couple will have $1038.426 to spend on their vacation.

4.) Cost of vacation is $9,384.44,this is the final amount,principal is$5859.37,time is 2 years,we have to find annual compound interest rate using the above formula which is as follows

9384.44=5859.37(1+interest rate)^2

9384.44/5859.37=(1+interest rate)^2

1.6016=(1+interest rate)^2

1.2656=1+interest rate

0.2656=interest rate

Interest rate =0.2656 or 26.56%

So couple needs to have 26.56% annual compound interest rate to meet vacation costs after 2 years from now.

5.) Cost of vacation or final amount required here is $12,000,principal is $7451.05,their compound annual interest rate is 10% or 0.1,we will put this information in above formula get time required as follows

12000=7451.05(1+0.1)^time in years

12000/7451.05=(1+0.1)^time in years

1.6105=(1.1)^time in years

log(1.6105)=log[(1.1)^time in years]

time in years=log(1.6105)/log(1.1)

=4.999

Thus it will take couple 5 years to go to the vacation.

Answer is complete.Thank you!