Question

Emilia and Liam are purchasing a home. They wish to save money for 12 years and purchase a house that has a value of $200,000 with cash. If they deposit money into an account paying 4% interest, compounded monthly, how much do they need to deposit each month in order to make the purchase? A. $1084.39 B. $1388.89 C. $409.86 D. $412.85 Andrew deposits $503.81 each month into an annuity account for his child's college fund in order to accumulate a future value of $90,000 in 12 years. How much of the $90,000 will Andrew ultimately deposit in the account, and how much is interest earned? A. Total deposited: $17,451.36 Interest earned: $72,548.64 B. Total deposited: $72,548.64 Interest earned: $90,000 C. Total deposited: $90,000 Interest earned: $17,451.36 D. Total deposited: $72,548.64 Interest earned: $17,451.36

          Emilia and Liam are purchasing a home. They wish to save money for 12 years and purchase a house that has a value of $200,000 with cash. If they deposit money into an account paying 4% interest, compounded monthly, how much do they need to deposit each month in order to make the purchase?

A. $1084.39
B. $1388.89
C. $409.86
D. $412.85

Andrew deposits $503.81 each month into an annuity account for his child's college fund in order to accumulate a future value of $90,000 in 12 years. How much of the $90,000 will Andrew ultimately deposit in the account, and how much is interest earned?

A. Total deposited: $17,451.36 Interest earned: $72,548.64
B. Total deposited: $72,548.64 Interest earned: $90,000
C. Total deposited: $90,000 Interest earned: $17,451.36
D. Total deposited: $72,548.64 Interest earned: $17,451.36

Show more…

Emilia and Liam are purchasing a home. They wish to save money for 12 years and purchase a house that has a value of 200,000 with cash. If they deposit money into an account paying 4% interest, compounded monthly, how much do they need to deposit each month in order to make the purchase?

A.1084.39
B. 1388.89
C.409.86
D. 412.85

Andrew deposits503.81 each month into an annuity account for his child's college fund in order to accumulate a future value of 90,000 in 12 years. How much of the90,000 will Andrew ultimately deposit in the account, and how much is interest earned?

A. Total deposited: 17,451.36 Interest earned:72,548.64
B. Total deposited: 72,548.64 Interest earned:90,000
C. Total deposited: 90,000 Interest earned:17,451.36
D. Total deposited: 72,548.64 Interest earned:17,451.36

Added by Christopher B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

07/07/2023

Step 1

The formula for the future value of an ordinary annuity is: FV = P * [(1 + r/n)^(nt) - 1] / (r/n) where: FV = future value of the annuity P = monthly deposit r = annual interest rate (in decimal form) n = number of times the interest is compounded per year t = Show more…

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Transcript

00:01 In this question we are given two questions.

00:03 So the first question we are given that in 12 years liam and emily need to save $200 ,000 to pay for house.

00:30 The rate of interest is rate of interest is given as 4 % compounded annually.

00:43 So it is not compounded annually but it is compounded monthly.

00:48 So it is compounded monthly.

00:51 We need to find out to find how much they need to deposit monthly into the account.

01:04 How much monthly deposit is needed in the account.

01:12 How much monthly deposit is needed in the account.

01:21 So for that we use the formula that future value is equal to present times 1 plus rate of interest is the power n minus 1 divided by the rate of interest.

01:34 So here rate of interest is equal to 4 % divided by 12 since the compounding is done on a monthly basis and there are 12 months in a year.

01:46 The future value is $200 ,000 and total time n is equal to 12 multiplied by 12.

02:01 So we have total 144 months.

02:05 Therefore the value of p would be on plugging the values we get 200 ,000 is equal to p 1 plus 0 .04 divided by 12 raised to the power 144 minus 1 divided by 0 .04 upon 12.

02:27 So on simplifying this we get p is equal to 200 ,000 times 0 .04 divided by 12 divided by 1 plus 0 .04 divided by 12 raised to the power 144 minus 1.

02:48 On simplifying this we get p is approximately equal to 108439 dollars.

02:58 So this is the final answer to our question...

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