Jamal wants to save 54,000 for a down payment on a home. How much will he need in an account wi

Jamal wants to save 54,000 for a down payment on a home....

Key Concepts

Compound Interest

Compound interest refers to the process where interest is calculated on both the initial principal and the accumulated interest from previous periods. This concept is fundamental in finance and is used to determine how investments grow over time when interest is reinvested.

Present Value Calculation

Present value calculation involves determining the amount of money that must be invested today to achieve a desired future sum, considering a given rate of return and time period. This concept is crucial for planning and evaluating financial goals under the influence of compound interest.

Annual Percentage Rate (APR)

APR is the annual rate charged for earning or borrowing money, expressed as a percentage. It represents the yearly cost of funds over the term of a loan or investment, excluding the effects of compounding, and is essential for comparing financial products.

Compounding Frequency

Compounding frequency refers to the number of times interest is applied to the investment balance within a certain period, such as daily, monthly, or annually. The frequency of compounding can significantly affect the growth of an investment due to the exponential nature of compound interest.

Transcript

00:01 All right, so in this question, jamal wants to say $54 ,000 for a down payment on a home.

00:08 How much will we need in this account with 8 .2 % apr compounding daily in order to reach his goal in five years? okay.

00:17 So we have to remember what the compounding equation is for this case.

00:21 For typical investments who use the formula, i think it would be a is equal to p times 1 plus r over.

00:31 N to the nt now a is the final amount right p is the initial deposit r is the apr the rate essentially n is how often is compounded so if it's compounded annually n would be one if it was semi -annually it would be two every day right it would be 365 because you're going by how many times per year basically so if it's daily there's 365 days in an average year so that's what we would include for and actually i won't put the number i'll put compounding rate and t will just be time so in this case i believe it's five years yep now we have everything except for how much we need to put in the count originally basically that means p right the initial amount how much should he put it initially in order for this to eventually get to fifty four thousand dollars which is a so we can just you know do some basic math and plug and plug everything in and to solve for p essentially.

01:44 So we have 54 ,000 is equal to p times one plus apr is r which is 8 .2 % remember 8 .2 % has to be in decimal form so we have to move the decimal over 2 to the left so we're left with 0 .082 and it's going to be over 365 because remember it's being compounded daily meaning 365 times per year.

02:11 So just forget about leap years and stuff just it would be 300, on a standard year.

02:19 And then it's going to be times n times t, so it's going to be times 365 times five, because it's five years.

02:28 And now we just do some math and just cancel everything out.

02:31 So let me solve everything in this parentheses first, and then from there we can divide both sides by that and get p by itself and everything else on the other side...

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