Question

Rae started saving money at an early age (10 years old). Each month her mom put the money in an account that compounded annually at 5.75%. Now Rae is 23 and has $6936.72. How much did she save each month? (Assume she saved for a full 13 years) Use the FV or PMT functions in excel.

Answer 1

She saved $30 monthly.

Solution-

We know that,

`\text{FV of annuity}=P[((1+r)^n-1)/(r)]`

Where,

P = periodic payment

r = rate per period

n = number of period

Here,

`FV\ of\ annuity=\$6936.72,\\\\P=?,\\\\r = 5.75\%\ annually=(5.75)/(12)\%\ monthly=(5.75)/(1200)\ monthly\\\\n=13\ years=13* 12=156\ months`

Putting the values,

`\Rightarrow 6936.72=P[\frac{(1+(5.75)/(1200))^(156)-1}{{(5.75)/(1200)}}]\\\\\\\Rightarrow P=\frac{6936.72}{[\frac{(1+(5.75)/(1200))^(156)-1}{{(5.75)/(1200)}}]}\\\\\\\Rightarrow P=(6936.72)/((2.107947-1)/(0.004792))\\\\\\\Rightarrow P=(6936.72)/((1.107947)/(0.004792))\\\\\\\Rightarrow P=30`

Therefore, she saved $30 monthly.