Question

Tyron is saving up money for a down payment on a motorcycle. He currently has $5648, but knows he can get a loan at a lower interest rate if he can put down $6355. If he invests the $5648 in an account that earns 6% annual, compounded monthly, how long will it take Tyron to accumulate the $6355

Answer 1

monthly time = 1.966

Step-by-step explanation:

given data

final amount = $6355

initial principal = $5648

rate = 6 %

solution

we get here time by this formula

amount = principal ×
`(1+r)^(t)` ............1

put here value and we get time t

6355 = 5648 ×
`(1+(0.06)/(12))^(12* t)`

1.125 =
`(1.005)^(12* t)`

take ln both side

ln 1.125 = ln
`(1.005)^(12* t)`

0.1177 = 12 × t × 4.9875 ×
`10^(-3)`

monthly time = 1.966