jim deposits $5,300 in a savings account that pays 4.25% apr. how much interest will he earn in 12 years?\n⑥…

jim deposits $5,300 in a savings account that pays 4.25% apr. how much interest will he earn in 12 years?\n⑥ how much principal would you have to deposit to earn $750 interest in 4 years at a rate of 3%?\n⑦ sharon estimates that it will cost $825,000 to send her daughter to college in 18 years. she has $50,000 to deposit in savings. what interest rate will she need so she has enough money?\n⑧ logan has a savings account that pays 2.85% int. he is depositing $2,500, and is wondering how long will it take to become $3,500?

jim deposits $5,300 in a savings account that pays 4.25% apr. how much interest will he earn in 12 years?\n⑥ how much principal would you have to deposit to earn $750 interest in 4 years at a rate of 3%?\n⑦ sharon estimates that it will cost $825,000 to send her daughter to college in 18 years. she has $50,000 to deposit in savings. what interest rate will she need so she has enough money?\n⑧ logan has a savings account that pays 2.85% int. he is depositing $2,500, and is wondering how long will it take to become $3,500?

Answer

Explanation:

Step1: Recall simple - interest formula

The simple - interest formula is $I = Prt$, where $I$ is the interest, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years.

Question 5

  • First, convert the interest rate from a percentage to a decimal. The annual percentage rate (APR) $r = 4.25%=0.0425$, the principal $P = 5300$, and the time $t = 12$ years.
  • Then, use the simple - interest formula $I=Prt$. $I=5300\times0.0425\times12$ $I = 5300\times0.51$ $I = 2703$

Question 6

  • Given $I = 750$, $t = 4$ years, and $r=3% = 0.03$.
  • Rearrange the simple - interest formula $I = Prt$ to solve for $P$. We get $P=\frac{I}{rt}$. $P=\frac{750}{0.03\times4}$ $P=\frac{750}{0.12}$ $P = 6250$

Question 7

  • The future value $A$ (the amount needed for college) is $A = 825000$, the principal $P = 50000$, and the time $t = 18$ years.
  • Using the simple - interest formula $A=P + Prt=P(1 + rt)$.
  • First, substitute the values into the formula: $825000=50000(1 + 18r)$.
  • Then, divide both sides by $50000$: $\frac{825000}{50000}=1 + 18r$. $16.5=1 + 18r$.
  • Subtract $1$ from both sides: $16.5−1 = 18r$. $15.5 = 18r$.
  • Solve for $r$: $r=\frac{15.5}{18}\approx0.8611$ or $86.11%$ (This is an extremely high and unrealistic rate in a real - world scenario. If we assume compound - interest, the problem would be more complex but more realistic).

Question 8

  • The principal $P = 2500$, the future value $A = 3500$, and the interest rate $r=2.85%=0.0285$.
  • Using the simple - interest formula $A=P+Prt=P(1 + rt)$.
  • First, substitute the values: $3500 = 2500(1+0.0285t)$.
  • Divide both sides by $2500$: $\frac{3500}{2500}=1 + 0.0285t$. $1.4=1 + 0.0285t$.
  • Subtract $1$ from both sides: $1.4−1 = 0.0285t$. $0.4 = 0.0285t$.
  • Solve for $t$: $t=\frac{0.4}{0.0285}\approx14.04$ years

Answer:

Question 5: The interest is $$2703$. Question 6: The principal is $$6250$. Question 7: The interest rate is approximately $86.11%$ (assuming simple - interest, which may be unrealistic). Question 8: It will take approximately $14.04$ years.