Part 1: Planning Ahead with Compound Interest Scenario: Suppose you have a new b
ID: 3137982 • Letter: P
Question
Part 1: Planning Ahead with Compound Interest Scenario: Suppose you have a new baby. You estimate that you need $ 100,000 for their college education when they are ready to go to college in 18 years. I. Assume you invest $10,000 in a mutual fund (eg. money market fund) at an APR of 7% compounded quarterly. How long, to the nearest tenth of a year, will it take the $10,000 to grow to $100,000? [Solve using both methods below.] Solve using Logarithmic Equations Solve using the T-84 TVM Solver (use a negative sign at the front of the number) PMT- FV - P/Y- Number of Years (nearest tenth): PMT (set at End) Number of Years (nearest tenth) (S pts.)
Explanation / Answer
1.The formula for the compound interest is A = P(1+r)n where P is the initial amount/principal, A is the future value , r is the rate of interest per period and is the number of periods. Here, P = $ 10000, r = 7/400 and A = $ 100000. Let it take t years for $ 10000 to grow to $ 100000 so that n = 4t.
Then, 100000 =10000(1+7/400)4t or, (407/400)4t = 100000/10000 = 10. Now, on taking logarithms of both the sides,we get log(1.0175)4t=log 10=1or,4tlog 1.0175 = 1. Hence t = 1/4log 1.0175= 1/[4(0.007534417897) = 33.18106368 = 33.2 years ( on rounding off to the nearest tenth).
2. No, the investment of $ 10000 will not grow to $ 100000 in 18 years as it will take over 33 years.
3. If A = $ 125000,r = 7/400 and t = 18 ( so that n = 18*4 = 72), then 125000 = P(1+7/400)72 so that P = 125000/(407/400)72 = 125000/(1.0175)72 = 125000/3.487209897 = $ 35845.28 (on rounding off to the nearest cent). Thus, $ 35845.28 has to be invested at 7 % APR , compounded quarterly , for the child to have $ 125000 in 18 years.