a) You have N$ 10,000 to invest, which you want to grow to N$ 100,000. If the bank
offers you an interest rate of 6% p.a. compounded monthly, how long must you
invest the money for (in months or years)? Round your answer to one decimal
place.
b) Instead of investing N$ 10,000, you decide to save N$ 1000 per month at the end of
each month. If the bank again offers you an interest rate of 6% p.a. compounded
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monthly, after how many years and months will you have N$ 100,000? Round your
answer to one decimal place.
We are not going to do your homework for you. It appears you are answer grazing. If you have some difficulty understanding how to do a problem, state the difficulty you are having, We are her to help students, not give answers to answer grazers.
=10000/100000*0.06
219
To solve both problems, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount
P = the principal (initial investment or monthly savings)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the time in years
a) To find out how long you must invest the money for to reach N$ 100,000 at an interest rate of 6% compounded monthly, we can rearrange the formula to solve for t:
100,000 = 10,000(1 + 0.06/12)^(12*t)
Dividing both sides by 10,000, we get:
10 = (1 + 0.06/12)^(12*t)
Taking the natural logarithm of both sides:
ln(10) = ln[(1 + 0.06/12)^(12*t)]
Using logarithm properties, we can bring down the exponent:
ln(10) = 12*t * ln(1 + 0.06/12)
Finally, solving for t, we have:
t = ln(10) / (12 * ln(1 + 0.06/12))
Using a calculator, we can find the value of t, which comes out to approximately 11.5 years.
b) To calculate how long it will take to reach N$ 100,000 by saving N$ 1,000 per month, we need to consider the monthly contributions as well. The formula can be modified as follows:
100,000 = 1,000[(1 + 0.06/12)^(12*t) - 1] / (0.06/12)
Simplifying,
100 = [(1 + 0.06/12)^(12*t) - 1] / (0.06/12)
Multiply both sides by (0.06/12):
100 * (0.06/12) = (1 + 0.06/12)^(12*t) - 1
0.005 = (1 + 0.06/12)^(12*t) - 1
Add 1 to both sides:
1.005 = (1 + 0.06/12)^(12*t)
Take the natural logarithm of both sides:
ln(1.005) = 12*t * ln(1 + 0.06/12)
Solving for t, we get:
t = ln(1.005) / (12 * ln(1 + 0.06/12))
Using a calculator, we find that t is approximately 17.8 years.
So, in part b, it will take approximately 17.8 years (or 17 years and 9 months) to reach N$ 100,000.