Question

Jacob needed money for some unexpected expenses, so he borrowed $5,890.25 from a friend and agreed to repay the loan in seven equal installments of $1,250 at the end of each year. The agreement is offering an implied interest rate of:
A) 14.85%


B) 9.57%


C) 11.00%


D) 12.98%


Jacob's friend Wilson, has hired a financial planner for advice on retirement. Considering Wilson's current expenses and expected future lifestyle chnages, the financial planner has stated that once Wislon crosses a threshold of $8,452,622 in savings, he will have enough money for retirement. Wilson has nothing saved for his retirement yet, so he plans to start depositing $40,000 in a retirement fund at a fixed rate of 11.00% at the end of each year. It will take _____ years for Wilson to reach his retirement goal.


A) 30.55 years


B) 41.24 years


C) 38.19 years


D) 25.97 years

Answer 1

Answer:

OPTION C i.e 11%

Option A i.e 30.55 year

Explanation:

we know that capital can be calculated as

$Capital = EMI \times PVIFA$

$capital = EMI \times \frac{(1+r))^n -1}{r (1+r)^n}$

from the data given in question we can calculate the value of r

so

$5890.2 = 1250 \times \frac{(1+r))^7 -1}{r (1+r)^7}$

$4.7122 = \frac{(1+r))^7 -1}{r (1+r)^7}$

solving for r we get

r = 11%

option C

we know that

$Total\ saving = cash flow \times FVIFA$

                      $= Cash\ flow \times \frac{(1+r)^n -1}{r}$

from the data given we can evealueate the value of n

$8,452,622 = 40,000 \times \frac{(1.11)^n -1}{0.11}$

$\frac{8452622}{40000}\times 0.11 = (1.11)^n -1$

solving for n we get

n = 30.55 year.

Option A