Question

A couple draw a plan of saving for their vacation in Europe. They save $200 at the end of each month for three years. If the cost of vacation is going to be ($9,384.44), and the interest rate is 11% compounded annually, would the couple have enough to cover their vacation at the end of the third year? 15. What must their annuity (A) be in order to make it to their vacation if the interest rate is 15% compounded semiannually. 16. What must their annuity (A) be in order to make it to their vacation if the interest rate is 13.75% compounded quarterly. 17. What must their annuity (A) be in order to make it to their vacation if the interest rate is 11.5% compounded monthly. 18. What must their annuity (A) be in order to make it to their vacation if the interest rate is 8.25% compounded weekly.

Answer 1

Results are below.

Step-by-step explanation:

Giving the following information:

Monthly saving= $200

Future value= $9,384.44

Number of years= 3

a) To calculate the Future Value, we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

FV= {2,400*[(1.11^3) - 1]} / 0.11

FV= $8,021.04

b) To calculate the semiannual deposit, we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= semiannual deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

i= 0.15/2= 0.075

n= 3*2= 6

A= (9,384.44*0.075) / [(1.075^6) - 1]

A= $1,295.47

c) i= 0.1375/4= 0.0344

n= 3*4= 12

A= (FV*i)/{[(1+i)^n]-1}

A= quarterly deposit

A= (9,384.44*0.0344) / [(1.0344^12) - 1]

A= $644.89

d) i= 0.115/12= 0.0096

n= 3*12= 36

A= (FV*i)/{[(1+i)^n]-1}

A= monthly deposit

A= (9,384.44*0.0096) / [(1.0096^36) - 1]

A= $219.46

e) i=0.0825/52= 0.0016

n= 3*52= 156

A= (FV*i)/{[(1+i)^n]-1}

A= weekly deposit

A= (9,384.44*0.0016) / [(1.0016^156) - 1]

A= $53.01