a compound interest problem: Susan has $50000 in her savings account...

[ansonguyguy]

I have trouble with the math problem below.

(ex) Susan has accumulated $50000 in her savings account. She plans to deposit $100 a month to her account which pays an annual interest rate of 6% compounded monthly. How much will she have in her account in 20 years?

This is how I do it. I am using two formulas.

(1) FV = D*[((1+r/n)^(nt))/(r/n)]

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

where FV is future value, D regular payment, r interest rate, n the number of compounding periods, t elapsed time, P principal and A the accumlated amount.

First, I plug these values in the first formula: D=100, r=0.06, n=12, t=20.

So, I get FV=$46204.09

Next, I plug these values in the second formula: P=FV+50000, r=0.06, n=12, t=20.

Therefore, A=$671789.39.

But, the answer key says $211714.31.

Could someone please explain how to do this problem? Thanks a lot.

 

[Deleted member 4993]

I have trouble with the math problem below.

(ex) Susan has accumulated $50000 in her savings account. She plans to deposit $100 a month to her account which pays an annual interest rate of 6% compounded monthly. How much will she have in her account in 20 years?

This is how I do it. I am using two formulas.

(1) FV = D*[((1+r/n)^(nt))/(r/n)]

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

where FV is future value, D regular payment, r interest rate, n the number of compounding periods, t elapsed time, P principal and A the accumlated amount.

First, I plug these values in the first formula: D=100, r=0.06, n=12, t=20.

So, I get FV=$46204.09

Next, I plug these values in the second formula: P=FV+50000, r=0.06, n=12, t=20.

Therefore, A=$671789.39.

But, the answer key says $211714.31.

Could someone please explain how to do this problem? Thanks a lot.

I am not sure - but I think the formula for future value is

(1) FV = D*[(1+r/n)^(nt) - 1]/(r/n)

 

[tkhunny]

I have trouble with the math problem below.

(ex) Susan has accumulated $50000 in her savings account. She plans to deposit $100 a month to her account which pays an annual interest rate of 6% compounded monthly. How much will she have in her account in 20 years?

This is how I do it. I am using two formulas.

(1) FV = D*[((1+r/n)^(nt))/(r/n)]

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

where FV is future value, D regular payment, r interest rate, n the number of compounding periods, t elapsed time, P principal and A the accumlated amount.

First, I plug these values in the first formula: D=100, r=0.06, n=12, t=20.

So, I get FV=$46204.09

Next, I plug these values in the second formula: P=FV+50000, r=0.06, n=12, t=20.

Therefore, A=$671789.39.

But, the answer key says $211714.31.

Could someone please explain how to do this problem? Thanks a lot.

Please demonstrate how you accumulated the $50,000 for 20 years. You may wish to consider that it is earning interest, not just sitting under a mattress.

Note the timeline. Please, ALWAYS draw one.

Start
Lump: $50,000
Stream: $0.00

20 Years
Lump: $50,000 + interest
Stream:20 years of payments + interest

After applying the first formula, you should have "20 years Stream 20 years of payments + interest." Why would you then decide to add $50,000 (which was 20 years ago) and then accumulate another 20 years?

What you have is not very close to what is asked. Check your formulas and give it another go. Only add funds that are at the same time.

 

[Peacock]

Next, I plug these values in the second formula: P=FV+50000, r=0.06, n=12, t=20.

I believe your problem is in the quote above. Note that A=P(1-r/n)^(tn) accumulates interest from time 0 until time t. By letting P=FV+50000 you are accumulating the FV+50000 for 20 years each.

Instead, simply let P=50000. This will give you the correct accumulated amount, A. Then simply add A and FV to get the solution value they gave.

 

[ansonguyguy]

Thank you, everyone!