Question

Find the interest rate needed for the sinking fund to reach the required amount. Assume that the compounding period is the same as the payment period.? (Note. A sinking fund is an account created to fund a future expense.? It's like a savings? account) ?$27 comma 456 to be accumulated in 5 ?years; quarterly payments of ?$1225

Answer 1

Answer:

so rate is 4.72 %

Step-by-step explanation:

Given data

time (t) = 5 year  = 5×4 = 20 quarterly

amount = $27456

principal = $1225

to find out

interest rate (r)

solution

we use here amount formula that is

amount = principal ($(1+r)^{t}$ -1 ) / r      .....................1

put all value principal , amount and time in equation 1 and we get rate

rate is r/4 because it is quarterly payment

amount = principal ($(1+r/4)^{t}$ -1 ) / r/4

27456 = 1225 ($(1+r/4)^{20}$ -1 ) / r/4

($(1+r/4)^{20}$ -1 ) / r/4  = 27456/ 1225

($(1+r)^{20}$ -1 ) / r  = 27456/ (1225 × 4)

($(1+r)^{20}$ -1 ) = r 27456/ (1225 × 4)

now by the tvm solver and amount  $27456

graph value

we get r = 0.0472

so rate is 4.72 %

Answer 2

Answer:

For figure out the interest rate we need to use the following formula

F=P(1+i)^n

n=5 years

F=$1225

P=$27

i=12.87% yearly