Answer to Question #207279 in Financial Math for Siphesihle

Question #207279
Moses invests R3 745,35 at the end of each month at an interest rate of 14,5% per year, compounded
monthly. How long will it take him to have R1 000 000,00? Give your answer to the nearest year.
1
Expert's answer
2021-08-04T13:06:56-0400

Calculating the number of months required (n):

FV of annuity=P×[(1+r)n1r]FV\space of\space annuity=P\times[\frac{(1+r)^n-1}{r}]


1,000,000=3,745.35×[(1+0.14512)n10.14512]1,000,000=3,745.35\times[(\frac{1+\frac{0.145}{12})^n-1}{\frac{0.145}{12}}]


1,000,0003,745.35×0.012083=(1.012083)n1\frac{1,000,000}{3,745.35}\times0.012083=(1.012083)^n-1


3.226223+1==(1.012083)n3.226223+1==(1.012083)^n ( now flip the equation and take log both sides)


n×log(1.012083)=log(4.226223)n\times log(1.012083)=log (4.226223)


n=log(4.226223)log(1.012083)n=\frac{log(4.226223)}{log(1.012083)}


n=119.99n=119.99


Where:

the future value of annuity = 1,000,000

the monthly payment (P) = 3,745.35

the monthly inteest rate =0.14512=\frac{0.145}{12}


Thus, the given annuity will take 119.99 months, i.e., 120 months rounded off, or 10 years to achieve 1,000,000.00. 

10 years


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment