Suppose you receive for graduation a gift of $1200 from your favorite relative. You are required to invest at least $800 of the gift in a no-withdrawal savings program for at least two years.

Question

Plan A: First Savings Bank (FSB) pays 6% interest, compounded annually on savings accounts. Employee's Credit Union (ECU) has options that allow you to choose your interest rate and how often your interest is compounded.

1. Determine how much you would have at the end of 2 years if you decided to invest $1000 at FSB (Answer for this one is $1123.60)
2. One of the options at ECU pays 5% interest annually and compounds interest quarterly. How much would your initial deposit there need to be to have the same amount that you would have after investing $1000 with FSB for 2 years?
3. Another option at ECU compounds interest monthly. If you invest $1000 compounded monthly with ECU, what interest rate would they have to pay for you to have the same amount that you would have after investing $1000 with FSB for 2 years?
4. If one plan at ECU pays 4.75% interest compounded bimonthly (every two months), and you invest $1000 in that plan, how long would it take for you to have the same amount that you would have after investing $1000 with FSB for 2 years?

Answer 1

1) A(t) = 1000(1 +.06)^t and A(2) = $1123.60.

2) 1123.60 = P (1 +.05/4)^4t and P = 1123.60/ (1.0125)⁸ = $1017.31.

3) 1123.60 = 1000(1 + r/12)^12t, [(12 + r)/12]²⁴ = 1.12360, (12 + r)/12 = (1.12360)^1/24 = 1.00487,

12 + r = 12.0584 and r = .0584 = 5.84%.

4) 1123.60 = 1000(1 + .0475/6)^6t, (1.0079167)^6t = 1.12360. Take log or ln of both sides: log[(1.0079167)^6t] = 6t log(1.0079167) = log(1.12360), 6t = 14.779, t = 2.463 years.