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Mohal is saving money and plans on making monthly contributions into an account earning a monthly interest rate of 
0.45%. If Mohal would like to end up with 
$19,000 after 30 months, how much does he need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.

A=d(((1+i)^(n)-1)/(i))

A= the future value of the account after 
n periods

d= the amount invested at the end of each period

i= the interest rate per period

n= the number of periods
Answer:

Mohal is saving money and plans on making monthly contributions into an account earning a monthly interest rate of 0.45% 0.45 \% . If Mohal would like to end up with $19,000 \$ 19,000 after 3030 months, how much does he need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.\newlineA=d((1+i)n1i) A=d\left(\frac{(1+i)^{n}-1}{i}\right) \newlineA= A= the future value of the account after n n periods\newlined= d= the amount invested at the end of each period\newlinei= i= the interest rate per period\newlinen= n= the number of periods\newlineAnswer:

Full solution

Q. Mohal is saving money and plans on making monthly contributions into an account earning a monthly interest rate of 0.45% 0.45 \% . If Mohal would like to end up with $19,000 \$ 19,000 after 3030 months, how much does he need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.\newlineA=d((1+i)n1i) A=d\left(\frac{(1+i)^{n}-1}{i}\right) \newlineA= A= the future value of the account after n n periods\newlined= d= the amount invested at the end of each period\newlinei= i= the interest rate per period\newlinen= n= the number of periods\newlineAnswer:
  1. Identify Given Values: Identify the given values from the problem.\newlineAA (future value of the account) = $19,000\$19,000\newlineii (interest rate per period) = 0.45%0.45\% per month, which is 0.00450.0045 in decimal form\newlinenn (number of periods) = 3030 months\newlineWe need to find the value of dd (the amount invested at the end of each period).
  2. Plug Values into Formula: Plug the given values into the formula to solve for dd. The formula is A=d×((1+i)n1)/iA = d \times \left(\left(1 + i\right)^{n} - 1\right) / i. We have A=$19,000A = \$19,000, i=0.0045i = 0.0045, and n=30n = 30.
  3. Calculate (1+i)n(1 + i)^n: Calculate the value inside the parentheses (1+i)n(1 + i)^n.(1+i)n=(1+0.0045)30(1 + i)^n = (1 + 0.0045)^{30} Use a calculator to find the value.(1+0.0045)301.142475(1 + 0.0045)^{30} \approx 1.142475
  4. Calculate ((1+i)n1)((1 + i)^n - 1): Calculate the numerator of the formula ((1+i)n1)((1 + i)^n - 1).
    ((1+i)n1)=1.1424751((1 + i)^n - 1) = 1.142475 - 1
    ((1+i)n1)0.142475((1 + i)^n - 1) \approx 0.142475
  5. Calculate Value of d: Calculate the value of d using the formula.\newlined=A((1+i)n1)/id = \frac{A}{\left(\left(1 + i\right)^n - 1\right) / i}\newlined=$19,000(0.142475/0.0045)d = \frac{\$19,000}{\left(0.142475 / 0.0045\right)}\newlineFirst, calculate the denominator of the fraction.\newline0.142475/0.004531.66110.142475 / 0.0045 \approx 31.6611
  6. Divide to Find d: Now, divide the future value AA by the result from Step 55 to find dd.d=$19,00031.6611d = \frac{\$19,000}{31.6611}d$600.18d \approx \$600.18Since we need to round to the nearest dollar, d$600d \approx \$600.

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