4 nelsons financial goal is to invest a sum of money at 4...

Nelson's financial goal is to invest a sum of money at 4% interest compounded monthly. If his goal is to have $20,000 at the end of 5 years, how much will he need to invest? (Assume rounding to the nearest penny.)

Transcript

00:01 So from the question, it is clear that the interest is compound interest, that is interest compounded monthly, and the rate and the goal, that is the final amount that the amount has to become is given and the time is also given.

00:14 So from those many values or those many given data, we can use the compound interest formula.

00:21 That is, i am just adding over here.

00:23 So this is the compound interest formula that is amount after day time, a will be equal to, that is a principal amount that is the amount that is like deposited first into one plus r r is the interest rate divided by n and is the number of times the interest will be compounding per unit time into n into t i can write so from the given data i'll be just adding all the given data from here so the rate was given as 4 percentage so r is equal to 4 percentage which is in decimal form i can write 0 .04 because 4 by 100 that is 0 .04 that is a rate of interest and it was given that if the goal is to have 20 ,000 that means amount that has to become that is a in this equation is equal to 20 ,000 and time is given as five years time is given as five years now we have to find what is the value of n so to find n it was given that the 4 % interest compounded monthly so in one year it is compounded monthly that is 12 times it will be compounding because in one year there is 12 months so n will be 12 now we have to find what is the value of p that is what is the amount that he has to deposit first or he has to invest first so we can write this formula 20 ,000 equal to p is what we have to find 1 plus rate was 0 .04 divided by 12 to the power of 12 into 5 i can write so it is very easy to find the value of p that is 20 ,000 equal to p into 1 .104 .104 divided by 12 is equal to something plus one i'll write whole raise to 12 into 5 so that value will become p into 1 .2209 and from this i can write the value of p is equal to 20 ,000 divided by that value 1 .220 so 1 .220 so 1 .2209...

Question

Nelson's financial goal is to invest a sum of money at 4% interest compounded monthly. If his goal is to have $20,000 at the end of 5 years, how much will he need to invest? (Assume rounding to the nearest penny.)

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