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If Jansen deposits $2 000, how long must he wait until your account has grown to $3,700?

Question:

If Jansen deposits $2 000, how long must he wait until your account has grown to $3,700?

Savings Account:

Savings account is a bank account that is intended for the client to save money and earn interest over time. Savings account can also be used directly to purchase goods or services instead of using cash.

Answer and Explanation:

Formula on calculating the required number of periods

{eq}Period=\dfrac{ln\bigg(\dfrac{FV}{PV}\bigg)}{ln(1+r)}\\ where:\\ FV=future~value\\ PV=present~value\\ ln=logarithmic~number\\ r=interest~rate\\ {/eq}

In this case, we need to make an interest rate assumption to determine the number of periods for the account to grow on a specific future value. Assuming that the interest rate of the account is 5%, then:

{eq}\begin{align*} Period&=\dfrac{ln\bigg(\frac{3,700}{2,000}\bigg)}{ln(1+.05)}\\ &=\dfrac{ln(1.82)}{ln(1.05)}\\ &=\dfrac{.615186}{.048790}\\ &=12.61 \end{align*} {/eq}

It would take 12.61 years for the $2,000 to grow to $3,700 in an account earnings 5% per year


Learn more about this topic:

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How to Calculate Interest Expense: Formula & Example

from Financial Accounting: Help and Review

Chapter 5 / Lesson 18
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