Answer to Question #210567 in Financial Math for Gomolemo

Question

Betty wants to invest a monthly sum of money in order to accumulate R100000 in seven years. How much must be the deposit monthly if her bank offers her an interest rate of 6% per annum compounded monthly? What if she was given an interest rate of 8%? Calculate

Answer 1

The PMT or monthly deposits required to accumulate $100,000 after 7 years at 6% would be as follows:

$PMT=\frac{\frac{r}{n}×FV}{({1+\frac{r}{n})^{t×n}-1}}$

Where,

FV is the future value of the amount to be accumulated ($100,000)

r is the interest rate (0.06)

t is the time period (7 years)

n is the number of compounding in a year (12 or monthly)

FV=$100000

r=0.06

t=7years

n=12 or monthly

$PMT=\frac{\frac{0.06}{12}×100000}{({1+\frac{0.06}{12})^{7×12}-1}}\\=\$960.86$

Thus, the PMT or required monthly payments are $960.86 to accumulate $100,000 in 7 years at 6%.

And, if the interest is changed to 8%, then the PMT or required monthly deposits to accumulate $100,000 in 7 years would be:

$PMT=\frac{\frac{0.08}{12}×100000}{({1+\frac{0.08}{12})^{7×12}-1}}\\=\$891.95$

Thus, the PMT or required monthly payments are $891.95 to accumulate $100,000 in 7 years at 8%.

 

Hence, she should deposit $960.86 and $891.95 monthly if the interest rate is 6% and 8% respectively