Question

You can afford monthly payments of $200 into an account that pays 3.3% compounded monthly. How long will it be until you have $12,000 to buy a boat?

Answer 1

$Future Value = Periodical Payments * \frac{(1+r)^{n}-1}{r}$

where r is the rate of return of 1 period i.e 3.3%/12 = 0.275% OR 0.00275

n is the no of compounding periods

$12,000= 200* \frac{(1+0.00275)^{n}-1}{0.00275}$

$(1+0.00275)^{n} = \frac{12000*0.00275}{200} +1$

Taking LOG both sides

n * log (1.00275) = log 1.165

n*0.00119 = 0.06633

n = 0.06633/ 0.00119

n = 55.75 years

It will take 55.75 years

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