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

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

Answer 2

so rate is 4.72 %

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 %