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David invested $350 in an account paying an interest rate of 3 % compounded
continuously. Jack invested $350 in an account paying an interest rate of 3%
compounded quarterly. After 5 years, how much more money would David have in
his account than Jack, to the nearest dollar?

Sagot :

mhanifa

Answer:

  • $0 difference

Step-by-step explanation:

David

  • Principal P = $350
  • Interest rate r = 3% = 0.03 PA compounded
  • Compound number = continuous
  • Time t = 5 years

Total in account after 5 years:

  • [tex]A=Pe^{rt}=350*e^{0.03*5} = 406.64[/tex]

Jack

  • Principal P = $350
  • Interest rate r = 3% = 0.03 PA compounded
  • Compound number n = 4
  • Time t = 5 years

Total in account after 5 years:

  • [tex]A = P(1+r/n)^{nt}=350(1+0.03/4)^{4*5}=406.41[/tex]

The difference in totals:

  • $406.64 - $406.41 = $0.23 ≈ $0 rounded to the nearest dollar

After 5 years Jack will have $0.66 more money in his account than David.

What is a compound interest?

This is a type of interest that is compounded after time period it is said to be compounded. After that particular period, the interest is calculated and then added with the principle. For the next duration, the interest is calculated on the sum.

Here, to find the amount of money after n years, we need to use the formula S = P(1 + r)ⁿ.

For David, S = sum of money after the total period of investment.

P = Principle = $350, r = rate of interest = 3% compounded annually, n = time period = 5 years.

Now, S = $350(1 + 3/100)⁵ = $350(1 + 0.03)⁵ = $350(1.03)⁵ = $405.75

Hence, after 5 years, David will have $405.75 in his bank account.

For Jack, S = sum of money after the total period of investment.

P = Principle = $350, r = rate of interest = 3% compounded quarterly, n = time period = 5 years.

Now, S = $350(1 + 3/ 4× 100)⁵ˣ⁴ = $350(1 + 0.0075)²⁰ = $350(1.0075)²⁰ = $406.41.

Hence, after 5 years, Jack will have $406.41 in his bank account.

Therefore, Jack will have $(406.41 - 405.75) = $0.66 more money than David.

Learn more about compound interest here: brainly.com/question/25857212

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