twins graduate from college together and start their careers. Twin 1 invests $15
ID: 3138642 • Letter: T
Question
twins graduate from college together and start their careers. Twin 1 invests $1500 at the end of each year for 10 years only (until age 35) in an account that earns 7%, compounded annually. Suppose that twin 2 waits until turning 40 to begin investing. How much must twin 2 put aside at the end of each year for the next 25 years in an account that earns 7% compounded annually in order to have the same amount as twin 1 at the end of these 25 years (when they turn 65)? (Round your answer to the nearest cent.)
Explanation / Answer
The future value of an annuity (F) is given by F = P[(1+r)n-1]/r, where P is the periodic payment, r is the rateof interest per period and n is the number of periods.
Here, in case of Twin 1, P = $ 1500, n = 10 and r = 0.07 so that F = (1500/0.07)[(1.07)10 -1] = (1500/0.07)*0.967151357 = $ 20724.67 ( on rounding off to the nearest cent).
In case of Twin 1, F = $ 20724.67, r = 0.07, n = 25 so that 20724.67 = (P/0.07)[ (1.07)25 -1]= (P/0.07)*4.42743264 so that P =(20724.67 )*0.07/4.42743264 = $ 327.67.
Thus, Twin 2 should put aside $ 327.67 at the end of each year for the next 25 years in an account that earns 7% compounded annually, in order to have the same amount as Twin 1 at the end of these 25 years.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.