You need $20,000 to make a down payment on a house. Your beginning balance in your checking account this month was $5,678. Your ending balance was $6,324. Assuming your account balance continues to grow at the same rate, how long until you have enough money to make the down payment?

Question

Mathematics

Odin Zhang

28 November, 08:29

You need $20,000 to make a down payment on a house. Your beginning balance in your checking account this month was $5,678. Your ending balance was $6,324. Assuming your account balance continues to grow at the same rate, how long until you have enough money to make the down payment?

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Answers (1)

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Alissa Compton · Answer 1

22.1649 months

Step-by-step explanation:

We begin by calculating the interest accruing to the principal amount in the bank account;

$6,324 - $5,678

= $646

646/5678 * 100

= 11.38 % pm

Now that know the interest rate, we calculate the amount of time it will take to accrue to $20,000

A = P (1 + rt)

Where:

A = Total Accrued Amount (principal + interest)

P = Principal Amount

r = Rate of Interest per year in decimal; r = R/100

t = Time Period involved in months or years

20000 = 5678 (1 + 0.1138t)

20000 = 5678 + 646.1564t

20000 - 5678 = 646.1564t

14,322 = 646.1564t

t = 14,322/646.1564

t = 22.1649