Question

An investment offers $10,000 at the end of each year for ten years. (a) If you can earn 5 percent annually, what is this investment worth today? (b) If you do not spend the annual payment but invest it at 5 percent, how much will you have after the ten years have lapsed?

Answer #1

**Given,**

**Annual payment (A) = $10000**

**No. of years (n) = 10 years**

**Solution :-**

**(a)**

**Interest rate (r) = 5% or 0.05**

**Present value = A/r x [1 - (1 +
r) ^{-n}]**

**= $10000/0.05 x [1 - (1 +
0.05) ^{-10}]**

**= $200000 x [1 - (1.05) ^{-10}]**

**= $200000 x [1 -**
**0.61391325354]**

**= $200000 x 0.38608674646 = $77217.35**

**This investment is worth $77217.35 today.**

**(b)**

**Interest rate (r) = 5% or 0.05**

**No. of years (n) = 10 years**

**Future value = A/r x [(1 + r) ^{n} -
1]**

**= $10000/0.05 x [(1 + 0.05) ^{10} -
1]**

**= $200000 x [(1.05) ^{10} - 1]**

**= $200000 x [1.62889462675 - 1]**

**= $200000 x 0.62889462675 = $125778.93**

**You will have $125778.93 after ten years.**

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