Answered

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Jazmine wants to have $500,000 in her
savings account when she retires. She
deposits $20,000 into an account that
earns 8% interest and is compounded
quarterly. How long will it take her to
reach her goal?

Sagot :

Answer:

40.6 years

Step-by-step explanation:

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

whereas

A = final amount

P = the principal amount

r = rate of interest

t = time in years

When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4n = number of times the amount is compounding.

So n = 4

A = P (1 + r/4)^4t

If A is 500,000, P is 20,000, r is 0.08

500000 = 20000(1 + 0.08/4)^4t

25 = (1+ 0.02)^4t

25 = (1.02)^4t

Take the log of both sides

ln 25 = 4t (ln 1.02)

4t = (ln 25)/(ln 1.02) = 162.55

so t = 162.55/4 = 40.6 years

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