Question

QUESTION 4 Find the amount of each payment to be made into a sinking fund so that enough money will be able to pay off a loan of $34,050 due in 9 years if money is earns 4.50% compounded annually. Assume this to be an ordinary annuity. A. $3,152.16 B. $2,770.95 C. $3,630.06 D. $3,184.39 QUESTIONS If Russell wanted to start making payments today, what would be the amount of each payment into a sinking fund so that enough money will be able to pay off a loan of $12,750 due in 10 years if money is earns 3.00% compounded annually. A. $1,392.06 B. $1,079.80 C. $1,218.48 D. $1,230.11

Answer 1

Answer 4:

Data given:

Rate of interest per annum, r = 4.5%

Future value of ordinary annuity, FV = $34050

Time period of investment (in years), t = 9 years

Frequency of payments in a year, n = 1

Amount of each annuity payment, M = ?

As we know, the formula for computing the future value of an ordinary annuity is given as -

$Future \ value, \ FV = M \frac{\left ( 1+\frac{r}{n} \right )^{nt}-1}{\frac{r}{n}}$

where M - amount of each annuity payment

r - rate of interest per annum

n - frequency of payments in a year

t - time period through which payments are made

Using the above formula, we can compute the amount of each payment for the annuity as -

$Future \ value, \ FV = M \frac{\left ( 1+\frac{r}{n} \right )^{nt}-1}{\frac{r}{n}}$

(1+ 0.0451(9) 1 -1 34050 = M 0.045

$\frac{34050 \times 0.045}{(1+0.045 )^{9}-1} = M$

$\frac{34050 \times 0.045}{(1.045 )^{9}-1} = M$

$\therefore \ M = 3152.16 \ \ \ (rounded \ to \ the \ nearest \ cent)$

Thus, the required amount of each payment is approximately $3152.16 .

Hence, the correct option is (A) .