How much money should be deposited in a bank paying a yearly interest rate of 2.75% compounded monthly so that after 10 years the accumulated amount will be 50, 000?

Question

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Answer 1

Let x be initial amount deposited.

Since there are 12 months in a year, a yearly interest rate of 2.75% means that the monthly interest rate is 2.75/12 percent. Thus, every month the amount grows by a factor of 1 + 0.0275/12.

There are 12*10=120 months in 10 years and (as we just established) after each month our capital grows by a factor of 1 + 0.0275/12. Hence, the amount after ten years would be:

x(1 + 0.0275/12)¹²⁰

Setting this amount equal to 50000 and solving for x, we obtain:

x = 50000/(1 + 0.0275/12)¹²⁰

Rounding to the nearest cent, we obtain x = $37990.56.