question 17 nan and neal are twins. nan invests $5,000 at age 25. neal invests $7,000 at age 30. suppose…

question 17 nan and neal are twins. nan invests $5,000 at age 25. neal invests $7,000 at age 30. suppose both investments can earn a compound annual interest rate of 7%. both twins retire at age 60 and neither adds nor withdraws funds prior to retirement. which of the following statement is correct? a nan will have more money than neal when they are 55 but less than neal after 55. b neal will have earned more interest than nan by their retirement. c if both nan and neal wait to age 70 to retire they will have equal amounts of savings. d nan will have more money than neal at any age between 25 and 60. e none of these are correct 1.5 points 9 of 25 questions remaining

question 17 nan and neal are twins. nan invests $5,000 at age 25. neal invests $7,000 at age 30. suppose both investments can earn a compound annual interest rate of 7%. both twins retire at age 60 and neither adds nor withdraws funds prior to retirement. which of the following statement is correct? a nan will have more money than neal when they are 55 but less than neal after 55. b neal will have earned more interest than nan by their retirement. c if both nan and neal wait to age 70 to retire they will have equal amounts of savings. d nan will have more money than neal at any age between 25 and 60. e none of these are correct 1.5 points 9 of 25 questions remaining

Answer

Explanation:

Step1: Calculate Nan's future - value

Nan invests $P_1 = 5000$ at age 25 and the money compounds for $n_1=60 - 25=35$ years at an annual interest rate $r = 0.07$. Using the compound - interest formula $A=P(1 + r)^n$, Nan's investment will be $A_1=5000(1 + 0.07)^{35}$.

Step2: Calculate Neal's future - value

Neal invests $P_2 = 7000$ at age 30 and the money compounds for $n_2=60 - 30 = 30$ years at an annual interest rate $r = 0.07$. Using the compound - interest formula $A = P(1 + r)^n$, Neal's investment will be $A_2=7000(1 + 0.07)^{30}$.

Step3: Compare the two amounts

Calculate $A_1=5000\times(1.07)^{35}\approx5000\times10.67658=53382.9$. Calculate $A_2=7000\times(1.07)^{30}\approx7000\times7.61226=53285.82$. So Nan will have more money than Neal when they retire at age 60.

Answer:

A. Nan will have more money than Neal when they are 55 but less than Neal after 55.