Respuesta :
Answer:
$3,342
Explanation:
Given that,
Borrowed amount = $50,000
Repay in 10 years(n)
Required Rate of return = 5%
Inflation rate = 3%
Future value = $50,000
Real rate of return, r:
= [tex]\frac{(1+Nominal\ interest) }{(1+Inflation\ rate)}-1[/tex]
= [tex]\frac{(1+0.05) }{(1+0.03)}-1[/tex]
= [tex]\frac{1.05}{1.03}-1\\[/tex]
= 1.01941748 - 1
= 0.019417 or 1.9417%
Real future value:
= [tex]\frac{Future\ value}{(1+ Inflation\ rate)^{n}}[/tex]
= [tex]\frac{50,000}{(1+ 0.03)^{10}}[/tex]
= [tex]\frac{50,000}{(1.34391638)}[/tex]
= $37,204.69
Annual payment is calculated as follows:
= [tex]\frac{[\frac{Future\ value}{[(1+r)^{n}-1}] }{1+r}[/tex]
= [tex]\frac{[\frac{37,204.69}{[(1+0.019417)^{10}-1}] }{1+0.019417}[/tex]
= 3341.94 or 3,342 (Approx)
Therefore, the initial deposit must be $3,342 to reach your $50,000 target.
The initial deposit must be $3,472.99 to enable you to reach your $50,000 target.
Here, we are to calculate the initial deposit to enable one to reach the $50,000 target
Given Information
Borrowed amount = $50,000
Repay in 10 years (n)
Required Rate of return = 5%
Inflation rate = 3%
Future value = $50,000
Firstly, we find the Real rate.
- The Formula for Real rate is [ ((1+nominal) / (1+inflation) ) - 1]
Real Rate = ((1+5%)/(1+3%)) - 1
Real Rate = 1.9417%
- Then we calculate the Real value of $50,000 by using inflation as discount rate
Read Value = $50,000*(1+3%) - 10
Read Value = $37,204.70
Then, we calculate the Annual payment to enable us know how large the initial deposit must be:
- The Formula for the Initial deposit (PMT) is (FV*r / ((1+r)n - 1) ) / (1+r)
Initial deposit = ($37,204.70*1.9417% / ((1 + 1.9417%)^10- 1) ) / (1 + 1.9417%)
Initial deposit = 722.4036599 / (0.21204492356/1.019417)
Initial deposit = $722.4036/ 0.2080060697)
Initial deposit = $3472.9931724
Initial deposit = $3,472.99
Therefore, the initial deposit must be $3,472.99 to enable you to reach your $50,000 target.
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