Question

You're prepared to make monthly payments of $340, beginning at the end of this month, into an account that pays 10 percent interest compounded monthly.

How many payments will you have made when your account balance reaches $24,678?

Answer 1

Hi,

here we already have the future value (FV) of the investment i.e. $24,678.

The investment amount is $340 p.m. So, P = $340

Interest rate (i) = 10% compounded monthly /12 =10% /12

So, FV = P((1+i)^t -1)/i)

=> FV/P = ((1+i)^t-1)/i)

=> (FV/P)*i = (1+i)^t -1

=> 1+(FV/P)*i = (1+i) ^t

=> t = ln (1+(FV/P)*i) / ln (1+i) = ln (1+ (24,678 / 340) * (10%/12)) / ln (1+10%/12) = ln (1.604853) / ln (1.008333)

To solve above you shall have to understand the natural logarithm table. am expecting you will be using this table instead of a calculator or excel

To find ln (1.60) you shall have to look for 1.6 in the rows below N, it starts from 1.0 , 1.1, 1.2 .... & go to the column 0 which starts adjacent of N as 0,1,2 3..... of the table & can find the intersection value of both row & col is 0.4700

To find ln (1.01) look for 1.0 in the rows below N & go to column 1 & find the intersection value as 0.0100

In financial calculator / excel there is inbuilt function ln() which can be used to get the values. Using excel ln() we can get the exact values to decimals

so in excel ln (1.60485) = 0.4730 & ln (1.0083) = 0.0083 which are nearby to what we found in the table

Now coming back to equation t in the given ques.

t = 0.4730 / 0.0083 = approx. 57 months.