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(i(1+i)n−1)A= the future value of the account after n periodsd= the amount invested at the end of each periodi= the interest rate per periodn= the number of periodsAnswer:
Q. 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(i(1+i)n−1)A= the future value of the account after n periodsd= the amount invested at the end of each periodi= the interest rate per periodn= the number of periodsAnswer:
Identify Given Values: Identify the given values from the problem.A (future value of the account) = $19,000i (interest rate per period) = 0.45% per month, which is 0.0045 in decimal formn (number of periods) = 30 monthsWe need to find the value of d (the amount invested at the end of each period).
Plug Values into Formula: Plug the given values into the formula to solve for d. The formula is A=d×((1+i)n−1)/i. We have A=$19,000, i=0.0045, and n=30.
Calculate (1+i)n: Calculate the value inside the parentheses (1+i)n.(1+i)n=(1+0.0045)30 Use a calculator to find the value.(1+0.0045)30≈1.142475
Calculate ((1+i)n−1): Calculate the numerator of the formula ((1+i)n−1). ((1+i)n−1)=1.142475−1 ((1+i)n−1)≈0.142475
Calculate Value of d: Calculate the value of d using the formula.d=((1+i)n−1)/iAd=(0.142475/0.0045)$19,000First, calculate the denominator of the fraction.0.142475/0.0045≈31.6611
Divide to Find d: Now, divide the future value A by the result from Step 5 to find d.d=31.6611$19,000d≈$600.18Since we need to round to the nearest dollar, d≈$600.