Suppose you want to accumulate $25,000 as down payment on a house and the best you can do is to put aside $200 a month. If you d

Question

4 years ago

5

Suppose you want to accumulate $25,000 as down payment on a house and the best you can do is to put aside $200 a month. If you d

eposit this amount at the beginning of each month in an account that credits 0.75% interest monthly, how long will it take you to attain your goal?

Mathematics

1 answer:

Sunny_sXe [5.5K] · Answer 1 · 2021-11-13T11:51:29+03:00

Answer:

It will take 88.2 months to accumulate the amount

Step-by-step explanation:

Given;

Future value of money, FV = $25,000

investment per compound period, P = $200

interest rate, i = 0.75% x 12 = 9%

The number of monthly installments required to amount to FV is given by;

$n = \frac{ln(FVi +cp)-ln(cp)}{ln(c+i)-ln(c)}\\\\ n = \frac{ln(25000*0.09 +200*12)-ln(200*12)}{ln(12+0.09)-ln(12)}\\\\n = \frac{8.4446 -7.7832}{2.4924-2.4849}\\\\n = 88.2 \ months$

Therefore, it will take 88.2 months to accumulate the amount.