You decide to put $2,000 in a savings account to save for a $3,000 downpayment on a new car. If the account has an interest rate of 4% per year and is compounded monthly, how long does it take until you have $3,000 without depositing any additional funds?

Question

Mathematics

Talan

16 January, 20:36

You decide to put $2,000 in a savings account to save for a $3,000 downpayment on a new car. If the account has an interest rate of 4% per year and is compounded monthly, how long does it take until you have $3,000 without depositing any additional funds?

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Answers (1)

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Danica Goodwin · Answer 1

Answer:it will take over 10 years

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

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

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 2000

r = 4% = 4/100 = 0.04

n = 12 because it was compounded monthly (12 times in a year)

A = 3000

Therefore,

3000 = 2000 (1+0.04/12) ^12 * t

3000/2000 = (1.0033) ^12t

1.5 = (1.0033) ^12t

Taking log of both sides

Log 1.5 = log (1.0033) ^12t

Log 1.5 = 12tlog (1.0033)

0.176 = 12t * 0.00143 = 0.01716t

t = 0.176/0.01716 = 10.26