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shepuryov [24]
3 years ago
11

Ben invested $20,000 into a money market account and took out $5,000 at the end of year 5. He found out at the end of 10 years t

hat he had as of $50,000 in the account. What is the annual interest rate Ben had earned on this investment
Business
1 answer:
Crazy boy [7]3 years ago
5 0

Answer:

r = 11.5%

Explanation:

Given data:

invested amount $20,000

withrawl amount after 5 year is $5000

Amount at the end of 10th yr is $50,000

present value  is given as

PV =\frac{ A}{(1 + r)^n}

where

A - amount after given n year

PV = \frac{5000}{(1 + r)^5} + \frac{50000}{(1 + r)^{10}}

20,000 =  \frac{5000}{(1 + r)^5} + \frac{50000}{(1 + r)^{10}}

 Let (1 + r)^5 = t

squaring on both side

(1 + r)^{10} = t^2

20,000 =  \frac{5000}{t} + \frac{50000}{t^2}

20 = \frac{5}{t} + \frac{50}{t^2}

20 t^2 - 5t - 50 = 0

solving for t we get

t = 1.711

so, r = 1.711^{1/5} -1 = 0.115 = 11.5\%

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