1. Your father invested a lump sum 25 years ago which earned 6.5% interest per y

Question

1. Your father invested a lump sum 25 years ago which earned 6.5% interest per year. Today, he gave you the proceeds of that investment which totaled $60,346. How much did your father originally invest?

2. What is the present value of $125,000 to be received 10 years from today if the discount rate is 7.5%?

3. Stuart needs $60,000 as a down payment for a house 5 years from now. He earns 3% per year on his savings. Stuart can either deposit one lump sum today for this purpose or he can wait a year and deposit a lump sum. How much additional money must he deposit if he waits for one year rather than making the deposit today?

Explanation / Answer

1. Calculation of original investment:

Formula to calculate Principal:

P = A / (1 + r/n)nt

P = Principal A = Future value = 60,346, r = Rate of Interest = 6.5%, n = Compounding = 1, t = Time = 25

P = 60,346 / (1 + 0.065 / 1)^1x25

P = 60,346 / 4.82769911

P = $12,500

So, the answer is $12,500

2. Present Value = FV / (1+r)^t

FV = 125,000, r = Discount = 7.5%, t = Time =10 Years

PV = 125,000 / (1+0.075)^10

PV = 125,000 / 2.06103156 = $60,650

3.PV of $60,000 received after 5 years:

PV = 60,000 / (1+0.03)^5 = 60,000 / 1.15927407 = $51,757

PV of $60,000 received after 4 years:

PV = 60,000 / (1+0.03)^4 = 60,000 / 1.12550881 = $53,309

Extra amount needed to deposit if he waits for one year = 53,309 - 51,757 = $1,552

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