You have $50,000 in savings for retirement in an investment earning a stated ann

Question

You have $50,000 in savings for retirement in an investment earning a stated annual rate of 5% compounded semi-annually. You aspire to have $1,000,000 in savings when you retire. Assuming you add no more to your savings, how many years will it take to reach your goal? Please round your answer to the nearest hundredth. Note that the HP 12c financial calculator rounds up the periods result to the next integer and will not give the correct answer to the nearest hundredth. Therefore, you should use Excel or a financial calculator that does provide decimal precision to the number of periods.

Explanation / Answer

Formula for compound interest:

A = P x (1 +r) n

A = Amount on maturity = $ 1,000,000

P = Principal = $ 50,000

r = Rate of interest = 5 % p.a. or 0.05/2 = 0.025 semiannually.

n = No. of periods

Putting the values in above formula, we get:

$ 1,000,000 = $ 50,000 x (1+0.025) n

$ 1,000,000 / $ 50,000 = (1+0.025) n

(1.025) n = 20

Taking logarithm of both sides we get,

n x log 1.025 = log 20

n x 0.01072386539 = 1.30102999566

n = 1.30102999566/0.01072386539

n = 121.32 periods or 121.32/2 = 60.6604964 or 60.66 years

60.66 years required to get the target fund.

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