Hi everyone. Today, we're going to use Texas BAII Plus Financial Calculator to solve a
problem involving compound interest. Let's look at an example. Bernard deposited $1,000
into an investment plan account on August 11, 2017. He then invested an additional $500
on May 29, 2018. What will be the balance in Bernard's investment account on
August 1st, 2025, if the plan earns a fixed rate of interest of 5% compounded daily?
Let's first draw a timeline. Bernard deposited $1,000 on August 11, 2017. And he then made an additional
deposit, $500, on May 29, 2018. We want to know how much money he will have on
August 1st, 2025. So we want know the maturity value at that point in time.
So in this question, first we have to look at between this time period, August 11, 2017
to May 29, 2018, because this 1,000 with compounding interest will be able to calculate a future
value for this $1,000. But then on the day of May 29, 2018 we made additional deposit.
So, 500 plus the future value of the $1,000, that'll become our new present value for the
second step, and we'll be able to find out what the future value is, which is the maturity
value for Bernard's investment. So, we'll look at two steps for this question.
Step one, we'll need to find out this future value of $1,000 investment. In order to use financial
calculator, we have to identify the seven variables.
So the present value, investment $1,000. Consider that's money leaving us, going to bank to
make the interest, we may use a negative sign there. Interest rate is 5% compounded daily.
Daily means C/Y would be 365. 365 compounding period every year. Periodic payment. In this
case, we do not have any monthly payments, quarterly payments, or daily investment. We
don't have any of those. Periodic payment is zero, and in this case we're talking about
payment per year, we'll just use the same number as C/Y, 365, because we do not have
periodic payments. N would be the time, so the compounding period between these two
dates. Now we'll have to use calculator to figure that out. Let's see. We'll turn on
the computer by pushing on and off button. We have two dates here. I can kind of see
that somewhat less than one year, but let's see the exact dates.
So we use second date function. So first date is August 11, 2017. We'll have to enter it
as 8.11.17 and push enter. You'll see August 11, 2017. Scroll down, you see the second
date, and it's 5.29, for May 29th, .18. Enter. You see May 29th, 2018. You scroll down, DBD.
You may see a number, but that's not your answer yet. That's probably from your previous
calculation. Make sure you push compute. Compute give us 291, so between these two dates are
291 days. Now remember definition for N. When we do not have periodic payment, N represents
number of compounding period. We compound daily, and there are 291 days, so 291 compounding
period. Now, if you see some questions that's not compounded daily, say it's compounded
monthly, then you make sure this 291 days you have to divide by 12, give you number
of months. But in this case we're fine with the number because it's compounded daily.
Now with all this information, let's calculate future value. Second P/Y, so P/Y is 365. Enter,
scroll down. C/Y is also 365. So for N is second quit, we'll get out the function, for
N is 291. 291 for N. Interest rate is five I/Y. PV is 1,000. We'll make it negative.
PMT's zero. Compute future value. Now, because this is only a middle step, so I will keep
all the decimals. I will only round at the end. So now we find out this future value.
We know this number plus 500 would be my present value for the second time period. Let's do
step two. Again, we'll be looking at the seven variables. So we know the PV is this number
plus $500. So I'll write down where this number come from at the bottom. So 1040.665366 plus
$500 is ... And that is where this PV come from. PMT is
still zero. We need to compute future value. Interest rate the same. P/Y C/Y is the same.
N. So N between these two dates, we need to find out. The days between dates.
So again, let's go to second date function. First date is 5.29.18. Enter. That's for May
29th, 2018. Scroll down for day two. Day two is 8.01.25. Enter. So that's August 1st, 2025.
You scroll down, you see 291. That's from previous calculation. So make sure you push
compute, give you the new answer. 2,621. Again, that's number of days between the two dates,
and because our interest compounded daily, so that is number of compounding periods for
our case. Now you see all those information hasn't changed, I can just enter the new information
and the rest are already stored on the calculator. So I'll override N. So second quit, or get
out the dates function. I go t o N is 2,621 for N. Everything else hasn't changed.
PV has changed. 1540.665366. I can make a negative for PV. You don't have to, but it's fine,
we'll make a negative. PMT's still zero. And let's compute. Future value is 2,206.11. Now
this time I round it to two decimal places. So our final answer how much Bernard will
have on August 1st, 2025 is $2,206 and 11 cents. Thank you for watching.