Julian is saving money and plans on making quarterly contributions into an account earning a quarterly interest rate of 1.875%. If Julian would like to end up with $17,000 after 10 years, how much does he need to contribute to the account every quarter, 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:

Question

Julian is saving money and plans on making quarterly contributions into an account earning a quarterly interest rate of  1.875%. If Julian would like to end up with  $17,000 after 10 years, how much does he need to contribute to the account every quarter, 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:

Bytelearn · Accepted Answer

Given Values: We are given: Future value of the account, A = $17,000 Quarterly interest rate, i = 1.875% or 0.01875 (as a decimal) Number of years, t = 10 Since contributions are made quarterly, there are 4 periods per year. Number of periods, n = 4 periods/year * 10 years = 40 periods We need to find the amount invested at the end of each period, d. Use the formula A = d(((1+i)^(n)-1)/(i)) to solve for d.Convert Interest Rate: First, convert the interest rate from a percentage to a decimal by dividing by 100. i = 1.875% / 100 = 0.01875Calculate Number of Periods: Next, calculate the number of periods over 10 years with quarterly contributions. n = 4 periods/year * 10 years = 40 periodsPlug Values into Formula: Now, plug the values of A, i, and n into the formula to solve for d. A = d(((1+i)^(n)-1)/(i)) $17,000 = d(((1+0.01875)^(40)-1)/(0.01875))Calculate Factor: Calculate the factor ((1+i)^(n)-1)/(i). ((1+0.01875)^(40)-1)/(0.01875) = ((1.01875)^(40)-1)/(0.01875) First, calculate (1.01875)^(40). (1.01875)^(40) ≈ 2.11356Subtract from Result: Subtract 1 from the result of (1.01875)^(40). 2.11356 - 1 ≈ 1.11356Divide by Interest Rate: Divide the result by i (0.01875). 1.11356 / 0.01875 ≈ 59.3904Solve for d: Now, solve for d using the calculated factor. $17,000 = d * 59.3904 d = $17,000 / 59.3904 d ≈ $286.26Round to Nearest Dollar: Since the question asks for the nearest dollar, round the result to the nearest whole number. d ≈ $286

Full solution

More problems from Compound interest

Related topics